Sample QuestionsArithmetic Progressions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Mark the correct alternative in the following: If the sum of three consecutive terms of an increasing $A.P$. is $51$ and the product of the first and third of these terms is $273,$ then the third term is:
Answer: C.
View full solution →Mark the correct alternative in the following:
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are:
Answer: A.
View full solution →Mark the correct alternative in the following:
The common difference of the A.P. is $\frac{1}{2\text{q}},\frac{1-2\text{q}}{2\text{q}},\frac{1-4\text{q}}{2\text{q}}, .....$ is
Answer: A.
View full solution →Mark the correct alternative in the following:
The next term of the A.P. $\sqrt{7},\sqrt{28},\sqrt{63},\ .....$
- A
$\sqrt{70}$
- B
$\sqrt{84}$
- C
$\sqrt{97}$
- ✓
$\sqrt{112}$
Answer: D.
View full solution →Mark the correct alternative in the following:
The common difference of the A.P. $\frac{1}{3},\frac{1-3\text{b}}{3},\frac{1-6\text{b}}{3}, ....$ is
- A
$\frac{1}{3}$
- B
$-\frac{1}{3}$
- ✓
$-\text{b}$
- D
$\text{b}$
Answer: C.
View full solution →Statement-1 (A): $-5,-\frac{5}{2}, 0, \frac{5}{2}, \ldots .$. is an A.P.
Statement-2 (R): The terms of an A.P. cannot have both positive and negative rational numbers.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: C.
View full solution →Statement-1 (A): $a, b, c$ are in A.P. if and only if $2 b=a+c$
Statement-2 (R): The sum of first $n$ odd natural numbers is $n^2$.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: B.
View full solution →Statement-1 (A): If $a_n$ denotes the nth term of the A.P. 2, 7, 12, 17, ..., then $a_{5160}-a_{2020}=15150$.
Statement-2 (R): If $a_n$ denotes the nth term of an A.P. with common difference $d$, then $a_p-a_q=(p-q) d$.
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement- 2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement- 1 is False, Statement- 2 is True.
Answer: A.
View full solution →Statement-1 (A): $\quad a, b, c$ arc in A.P. iff $2 b=a+c$.
Statement-2 (R): In an A.P. the sum of the terms cquidistant from the beginning and the end is aluays same and is equal to the sum of first and least term.
- A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- ✓
Statement-1 and Statement- 2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement- 1 is False, Statement- 2 is True.
Answer: B.
View full solution →Statement-1 (A): The sum of the $n$ terms of the A.P. $1,5,9,13, \ldots$ is $2 n^2+n$.
Statement-2 (R): Let $S_n$ denote the sum of $n$ terms of an A.P. with first term a and common difference $d$ such that $d=2 a$. Then for any natural number $m, \frac{S_{m n}}{S_m}$ is independent of $m$.
- A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement- 2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- ✓
Statement- 1 is False, Statement- 2 is True.
Answer: D.
View full solution →If the ratio of the sums of first n terms of two A.P.s is $\frac{5 n+13}{7 n+27}$ then the ratio of their 4th terms is __________.
View full solution →If $S_n=n(4 n+1)$ is the sum of in terms of an A.P., then its common difference is __________.
View full solution →If the $n^{\text {th }}$ terms of two A.P.s: 9, 7, 5.... and 24, 21, 18, ... are the same, then the value of n is __________.
View full solution →Two arithmetic progressions have the same common difference. Their first terms are A and B respectively. The difference between their $n^{\text {th }}$ terms is __________.
View full solution →If 7 times the$7^{\text {th }}$ term of an A.P. is equal to 11 times its $11^{ th }$ term, then the value of its $18^{\text {th }}$ term is __________.
View full solution →Determine the A.P. whose third term is 5 and seventh term is 9.
In an A.P. if the sum of third and seventh term is zero, find its 5th term.
Find the common difference of the Arithmetic progression
$\frac{1}{a}, \frac{3-a}{3 a}, \frac{3-2 a}{3 a}, \ldots \ldots(a \neq 0)$
View full solution →How many two digits numbers are divisible by 3?
Find the sum of the first 10 multiples of 3.
Which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.
$3, 3, 3, 3, .....$
View full solution →Find the sum of the first $25$ terms of an $A.P$. whose $n^{th}$ term is given by $a_n = 2 - 3n.$
View full solution →Find the sum:
$18+15\frac{1}{2}+13\ + ..... \ +\Big(-49\frac{1}{2}\Big)$
View full solution →The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P. whose first term is -30 and common difference is 8. Find n.
Find the $8^{th}$ term from the end of the $A.P. 7, 10, 13,... 184.$
View full solution →The general term of a sequence is give by $a_n=-4 n+15$. Is the sequence an A.P.? If so, find its $15^{\text {th }}$ term and the common difference.
View full solution →Find:$9^{th}$ term of the A.P. $\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4}, .....$
View full solution →Sum of 13 terms of the A.P. -6, 0, 6, 12, .....
Find the sum of the first 15 terms of each of the following sequences having $n ^{\text {th }}$ term as:
$b_{n}=5+2 n$
View full solution →Find the sum of the first 15 terms of each of the following sequences having $n^{th} $term as:
$y_n = 9 - 5n.$
View full solution →How many terms are there in the A.P.?
$-1,\frac{5}{6},\frac{2}{3},\frac{1}{2}, .....\frac{10}{3}.$
View full solution →The $24^{\text {th }}$ term of an A.P. is twice its $10^{\text {th }}$ term. Show that its $72^{\text {nd }}$ term is 4 times its $15^{\text {th }}$ term.
View full solution →All integers from 1 to 500 which are multiplies of 2 or 5.
The $26^{th}, 11^{th}$ and last term of an A.P. are 0, 3 and $-\frac{1}{5},$ respectively. Find the common difference and the number of terms.
View full solution →Find the sum of the following arithmetic progressions:$\frac{\text{x}-\text{y}}{\text{x}+\text{y}}\frac{3\text{x}-2\text{y}}{\text{x}+\text{y}}\frac{5\text{x}-3\text{y}}{\text{x}+\text{y}}, .....\text{ to n terms.}$
View full solution →View full solution →View full solution →View full solution →Do you know old clothes which are thrown as waste not only fill the landfill site but also produce very harmful greenhouse gas. So, it is very important that we reuse old clothes in whatever way we can. The picture given below on the right, shows a footmat (rug) made out
of old $t$-shirts yarn. Observing the picture, you will notice that a number of stitches in circulat rows are making a pattern : $6,12,18,24, \ldots$
Based on the above information, answer the following questions:
(i) Check whether the given pattern forms an AP. If yes, find the common difference and the next term of the AP.
(ii) Write the $n^{\text {th }}$ term of the AP. Hence, find the number of stitches in the $10^{\text {th }}$ circular row. View full solution →Rishi wants to buy a car and plans to take loan from a bank to buy the car. He pays his total loan of ₹ $1,180,000$ by paying every month starting with the first instalment of ₹ $10,000$. If he increases the instalment by ₹ $1000$ every month answer the following:
(i) The amount paid by Rishi in $30^{\text {th }}$ instalment, is
(a) ₹ 39,000 $\qquad$ (b) ₹ 35,000 $\qquad$ (c) ₹ 37,000 $\qquad$ (d) ₹ 36,000
(ii) The amount paid by Rishi in 30 instalments, is
(a) ₹ 370,000 $\qquad$ (b) ₹ 735,000 $\qquad$ (c) ₹ 753,000 $\qquad$ (d) ₹750,000
(iii) After paying $30^{\text {th }}$ instalment the amount still to be paid is
(a) ₹ 455,000 $\qquad$ (b) ₹ 490,000
(c) ₹ 445,000 $\qquad$ (d) ₹ 540,000
(iv) If the loan is to be repaid in 40 instalments, then amount paid in the last instalment is
(a) ₹ 49,000 $\qquad$ (b) ₹ 39,000
(c) ₹ 59,000 $\qquad$ (d) ₹ 94,000 View full solution →
