MCQ 11 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The $n\ '$ term of a sequence is $3n - 2$. It is an $A.P.$
Reason : A sequence is not an $A.P.$ ifitsn is not a linear expression in $n.$
- ✓
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong siatement.
- D
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: A. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
View full question & answer→MCQ 21 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : Arithmetic between $8$ and $12$ is $10.$
Reason : Arithmetic between two numbers $'a\ ’$ and $'b\ '$ is given as $\frac{\text{a}+\text{b}}{2}.$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
Both are correct and Reason is the correct explanation for the Assertion.
View full question & answer→MCQ 31 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If $n ^{\text {th }}$ term of an $A.P$. is $7-4 n$, then its common differences is $-4 $.
Reason: Common difference of an $A.P$. is given by $d=a_{n+1}-a_n$.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
Both are correct. Reason is the correct explanation.
Both are correct. Reason is the correct explanation.
Assertion, $a_n=7-4 n$
$d=a_{n+1}-a_n$
$=7-4(n+1)-(7-4 n)$
$=7-4 n-4-7+4 n=-4$
View full question & answer→MCQ 41 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The sum of the first $n$ terms of an $AP$ is given by $S_n=3 n^2-4 n$. Then its $n^{th}$ term $a_n=6 n-7$
Reason : $n^{th}$ term of an $AP,$ who sum to $n$ terms is $S_n$, is given by $a_n=S_{n-1}$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
$n^{th}$ term of an $AP$ be $a_n=S_n-S_{n-1}$
$a_n=3 n^2-4 n-3(n-1)^2+4(n-1)$
$a_n=6 n-7$
So, both $A$ and $R$ are correct and $R$ explains $A$.
View full question & answer→MCQ 51 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : Three consecutive terms $2k + 1, 3k + 3$ and $5k - 1$ form an $AP$ than is equal to $6.$
Reason : In an $AP , a, a + d, a + 2d,....., n $ terms of the $AP$ be $\text{s}_\text{n}=\frac{\text{n}}{2}(2\text{a}+(\text{n-1})\text{d})$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- ✓
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is tru
AnswerCorrect option: B. Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
For $2k + 1, 3k + 3$ and $5k - 1$ to form an $AP$
$(3k + 3) - (2k + 1) = (5k - 1) - (3k + 3)$
$k + 2 = 2k - 4$
$2 + 4 = 2k - k = k$
$k = 6$
So, both $A$ and $R$ are correct but $R$ does not explain $A$.
View full question & answer→MCQ 61 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The $10^{th}$ term from the end of the $A.P. 7, 10, 18, ...., 184$ is $163$.
Reason : In an $A.P$. with first term $a,$ common difference $d$ and last term $l,$ the $n^{th}$ term from the end is $l - (n - 1)d$.
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong siatement.
- ✓
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: D. Assertion is wrong statement but Reason is correct statement.
Assertion is wrong statement but Reason is correct statement.
Clearly, Reason is correct.
Now, $10^{\text {th }}$ term from end
$=1-( n -1) d$
$=184-(10-1) 3=184-27=157$
View full question & answer→MCQ 71 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : Common difference of the $AP -5, -1, 3, 7,$
Reason : Common difference of the $AP , a, a + d, a + 2d,.........$ is given by $d = 2^{nd}$ term $- 1^{st}$ term.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
Common difference $, d = -1 - 1(-5) = 4$
So, both $A$ and $R$ are correct and $R$ explains $A$
View full question & answer→MCQ 81 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : Common difference of an $AP$ in which $a _{21}- a _7=84$ is $14$.
Reason : $n$ th term of $AP$ is given by $a _{ n }= a +( n -1) d$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true
Assertion $(A)$ is false but reason $(R)$ is true
We have $ a_n=a+(n-1) d$
$a_{21}-a_7=\{a+(21-1) d\}-\{a+(7-1) d\}=84$
$a+20 d-a-6 d=84$
$14 d=84$
$\text{d}=\frac{84}{14}=6$
$\text{d}=6$
So, $A$ is incorrect but $R$ is correct
View full question & answer→MCQ 91 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason $( s )\ ( R )$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The common difference of the $A.P. 19, 18, 17, ....$ is $1.$
Reason: Let $a_1, d_2, a_3, a_4, \ldots$ is an $A.P.$ Then, common difference of this $A.P$. will be the difference between any two consecutive terms, i.e., common difference $(d)=a_2-a_1$ or $a_3-d_2$ or $a_1-a_3$ and so on.
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong siatement.
- ✓
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: D. Assertion is wrong statement but Reason is correct statement.
Assertion is wrong statement but Reason is correct statement.
Clearly, Reason is correct.
Given, $A.P$. is $19,18,17, \ldots$
Here, $a_1=19, a_2=18, a_3=17$ and so on.
$\therefore$ Common difference $(d) = a _2- a _1=18-19=-1$
View full question & answer→MCQ 101 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : Let the positive numbers $a, b, c$ be in $A.P., \frac{1}{\text{bc}},\frac{1}{\text{ac}},\frac{1}{\text{ab}}$ are also in $A.P.$
Reason : If each term of an $A.P$. is divided by abc, then the resulting sequence is also in $A.P$. are also in $A.P.$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
View full question & answer→MCQ 111 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If $a, b, c$ are in $A.P.,$ then $\frac{1}{\text{bc}},\frac{1}{\text{ac}},\frac{1}{\text{ab}}$ are also in $A.P.$
Reason : If a constant is added to each term of an $A.P.,$ then the resulting pattern of numbers is also an $A.P.$
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- ✓
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong siatement.
- D
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: B. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
$\because a, b, c$ are in $A.P. .. 2b = a + c$
Now $,\frac{1}{\text{bc}}+\frac{1}{\text{ab}}$
$=\frac{\text{a+}\text{c}}{\text{abc}}=\frac{2\text{b}}{\text{abc}}=\frac{2}{\text{ac}}$
$\text{So},\frac{1}{\text{bc}},\frac{1}{\text{ca}},\frac{1}{\text{ab}}$ are in $A.P.$
View full question & answer→MCQ 121 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If the first term of an $A.P$. is $4,$ last term is $81$ and the sum of the given terms is $510$. Then, there are $12$ terms in the given $A.P.$
Reason : If a is the first term, $l$ is the last term and $n$ is the number of terms of an $A.P.,$ then $\text{s}_\text{n}=\frac{\text{n}}{2}(\text{a}+\text{l})$
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong siatement.
- ✓
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: D. Assertion is wrong statement but Reason is correct statement.
Let $n$ be the number of terms.
We have, $\text{s}_\text{n}=\frac{\text{n}}{2}(\text{a}+\text{l})$
$\Rightarrow\frac{\text{n}}{2}(4+81)=510$
$\Rightarrow\text{n}=\frac{510\times2}{85}=12.$
View full question & answer→MCQ 131 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : Sum of first $10$ terms of the arithmetic progression $-0.5, -1.0, -1.5, ..........$ is $27.5$
Reason : Sum of $n$ terms of an $A.P.$ is given as $\text{s}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n-1)}\text{d}]$ where $a =$ first term, $d =$ common difference.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
Assertion,
$\text{s}_\text{n}=\frac{10}{2}[2(-0.5)+(10-1)+(-0.5)]$
$=5[-1-4.5]$
$=5(-5.5)=27.5$
View full question & answer→MCQ 141 Mark
Statement A (Assertion) : If the first term of an A.P. is 4, last term is 81 and the sum of the given terms is 510. Then, there are 12 terms in the given A.P.
Statement R (Reason) : If $a$ is the first term, $l$ is the last term and $n$ is the number of terms of an A.P., then $S_n=\frac{n}{2}(a-l)$.
- A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- ✓
Assertion (A) is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion (A) is true but reason $(R)$ is false.
(c) : Clearly, Reason is false.
Let $n$ be the number of terms.
We have, $S_n=\frac{n}{2}(a+l)$
$
\Rightarrow \quad \frac{n}{2}(4+81)=510 \Rightarrow n=\frac{510 \times 2}{85}=12 \text {. }
$
$\therefore \quad$ Assertion is true.
View full question & answer→MCQ 151 Mark
Statement A (Assertion): Sum of first 20 multiples of 4 is 480 .
Statement R (Reason) : In an A.P., sum of $n$ terms, $S_n=\frac{n}{2}[a+l]$ where, $n, a$ and $l$ are number of terms, first term and last term respectively.
- A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion (A) is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
(d): Clearly, Reason is true.
Now, first 20 multiples of 4 are $4,8,12, \ldots, 80$
Here, $a=4, d=4, l=80$
$
\begin{aligned}
\therefore \quad S_{20} & =\frac{20}{2}[4+80] \quad\left[\because S_n=\frac{n}{2}[a+l]\right] \\
& =10(84)=840
\end{aligned}
$
$\therefore \quad$ Assertion is false.
View full question & answer→MCQ 161 Mark
Statement $A ($Assertion$):$ The ninth term of an $A.P.$ is equal to seven times the second term and twelfth term exceeds five times the third term by $2.$ Then the first term is $1.$
Statement $R ($Reason$):$ If $S_n$ and $S_{n-1}$ are the sum of first $n$ terms and $(n-1)$ terms of an $A.P.,$ then $n^{\text {th }}$ term, $a_n=S_{n-1}-S_n$.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
- B
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion $(A).$
- ✓
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion $(A)$ is true but reason $(R)$ is false.
Clearly, Reason is false.
Let the first term and common difference of an $A.P.$ be $' a\ '$ and $' d\ ',$ respectively.
According to the question, $a_9=7 a_2$
$\Rightarrow a+8 d=7(a+d)$
$\Rightarrow a+8 d=7 a+7 d$
$\Rightarrow d=6 a\ldots(i)$
Also, $a_{12}-5 a_3=2 ($Given$)$
$\Rightarrow \quad(a+11 d)-5(a+2 d)=2$
$\Rightarrow a+11 d-5 a-10 d=2$
$\Rightarrow d-4 a=2$
$\Rightarrow 6 a-4 a=2[$Using $(i)]$
$\Rightarrow 2 a=2$
$\Rightarrow a=1$
$\therefore$ Assertion is true.
View full question & answer→MCQ 171 Mark
Statement A (Assertion) : The common difference of the A.P. 19, 18, 17, ... is 1.
Statement R (Reason) : Let $a_1, a_2, a_3, a_4, \ldots$ is an A.P. Then, common difference of this A.P. will be the difference between any two consecutive terms, i.e., common difference $(d)=$ $a_2-a_1$ or $a_3-a_2$ or $a_4-a_3$ and so on.
- A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion (A) is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
(d) : Clearly, Reason is true.
Given, A.P. is $19,18,17$, ...
Here, $a_1=19, a_2=18, a_3=17$ and so on.
$\therefore \quad$ Common difference $(d)=a_2-a_1=18-19=-1$
$\therefore \quad$ Assertion is false.
View full question & answer→MCQ 181 Mark
Statement A (Assertion) : The $10^{\text {th }}$ term from the end of the A.P.7, 10, 13, ..., 184 is 163 .
Statement R (Reason) : In an A.P. with first term $a$, common difference $d$ and last term $l$, the $n^{\text {th }}$ term from the end is $l-(n-1) d$.
- A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion (A) is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
(d) : Clearly Reason is true.
Now, $10^{\text {th }}$ term from end $=l-(n-1) d$
$
=184-(10-1) 3=184-27=157
$
$\therefore \quad$ Assertion is false.
View full question & answer→MCQ 191 Mark
Statement A (Assertion): The $n^{\text {th }}$ term of a sequence is $3 n-2$. It is an A.P.
Statement R (Reason) : A sequence is not an A.P. if its $n^{\text {th }}$ term is not a linear expression in $n$.
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion (A) is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
(a) : Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
View full question & answer→MCQ 201 Mark
Statement A (Assertion) : If $a, b, c$ are in A.P., then $\frac{1}{b c}, \frac{1}{c a}, \frac{1}{a b}$ are also in A.P.
Statement R (Reason) : If a constant is added to each term of an A.P., then the resulting pattern of numbers is also an A.P.
- A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion (A) is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: B. Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
(b) : $\because a, b, c$ are in A.P. $\therefore 2 b=a+c$
Now, $\frac{1}{b c}+\frac{1}{a b}=\frac{a+c}{a b c}=\frac{2 b}{a b c}=\frac{2}{a c}$
So, $\frac{1}{b c}, \frac{1}{c a}, \frac{1}{a b}$ are in A.P.
Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
View full question & answer→MCQ 211 Mark
Statement A (Assertion) : The numbers $4,1,-2,-5, \ldots$ are in A.P.
Statement R (Reason) : An A.P. is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first two terms.
- A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- ✓
Assertion (A) is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion (A) is true but reason $(R)$ is false.
(c) : Clearly, statement-II is false.
Now, given numbers are $4,1,-2,-5, \ldots$
Here, $a_1=4, a_2=1, a_3=-2, a_4=-5, \ldots$
$
\begin{aligned}
\therefore \quad & a_2-a_1=1-4=-3, a_3-a_2=-2-1=-3, \\
& a_4-a_3=-5-(-2)=-3, \ldots
\end{aligned}
$
Now, $a_2-a_1=a_3-a_2=a_4-a_3=\ldots . .=-3$
$\therefore$ Givennumbers are in A.P.since ithas samecommon difference.
View full question & answer→MCQ 221 Mark
Statement $A ($Assertion$)$ : If $a_7-a_{11}=300$, then $d=-75$.
Statement $R ($Reason$) : n^{\text {th }}$ term of an $A.P. =a+$ $(n-1) d$, where $a, d$ and $n$ are first term, common difference and number of terms respectively.
- ✓
Both assertion $(A)$ and reason $( R )$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
- B
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion $(A).$
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $( R )$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
Clearly, statement$-II$ is true.
Now, $a_7-a_{11}=300$
$\Rightarrow(a+6 d)-(a+10 d)=300 \left[\because a_n=a+(n-1) d\right]$
$\Rightarrow-4 d=300$
$\Rightarrow d=-75,$ which is true.
View full question & answer→