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.
Choose the correct answer from the given four options:
The famous mathematician associated with finding the sum of the first 100 natural numbers is:
Answer: A.
View full solution →Choose the correct answer from the given four options: The list of numbers $- 10, – 6, – 2, 2,...$ is:
- A
An $AP$ with $d = -16$
- ✓
An $AP$ with $d = 4$
- C
An $AP$ with $d = -4$
- D
Not an $AP$
Answer: B.
View full solution →Choose the correct answer from the given four options: In an $A P$ if $a=1, a_n=20$ and $S_n=399$, then $n$ is:
Answer: C.
View full solution →Choose the correct answer from the given four options: What is the common difference of an $AP$ in which $a_{18}-a_{14}=32 ?$
Answer: A.
View full solution →Choose the correct answer from the given four options: If the common difference of an $AP$ is $5,$ then what is $a_{18}-a_{13} ?$
Answer: C.
View full solution →Which of the following form an AP? Justify your answer.
1, 1, 2, 2, 3, 3, .....
Which of the following form an AP? Justify your answer.
11, 22, 33, .......
Which of the following form an AP? Justify your answer.
$\frac{1}{2},\frac{1}{3},\frac{1}{4},... $
View full solution →Which of the following form an AP? Justify your answer.
-1, -1, -1, -1 ...
Which of the following form an AP? Justify your answer.
$2, 2^2, 2^3, 2^4, .......$
View full solution →The taxi fare after each km , when the fare is Rs. $15$ for the first km and Rs. $8$ for each additional km , does not form an $AP$ as the total fare (in Rs.) after each km is $15,8,8,8.........$ Is the statement true? Give reasons.
View full solution →Justify whether it is true to say that the following are the nth terms of an $AP: 3n^2 + 5$
View full solution →Justify whether it is truw to say that $-1,\frac{-3}{2},-2,\frac{5}{2},......$ froms an A.P. as $a_2 - a_1 = a_3 - a_2$
View full solution →If the $9^{\text {th }}$ term of an AP is zero, prove that its $29^{\text {th }}$ term is twice its $19^{\text {th }}$ term.
View full solution →How many terms of the $AP -15, -13, -11, .......$. are needed to make the sum $-55$? Explain the reason for double answer.
View full solution →For the A.P: $-3,-7,-11$, ........ can we find directly $a_{30}-a_{20}$ without actually finding $a_{30}$ and $a_{20}$ ? Give reasons for your answer.
View full solution →Write the first three terms of the APs when a and d are as given below: $a = -5, d = -3$
View full solution →In which of the following situations, do the lists of numbers involved form an AP Give reasons for your answers:
The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is Rs. 250, and it increases by Rs. 50 for the next higher class.
If $s_n$ denotes the sum of first n terms n terms of an AP, prove that:
$S_{12} = 3(S_8 - S_4).$
View full solution →Find the-
sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.
If $a_n=3-4 n$, show that $a_1, a_2, a_3, \ldots \ldots .$. from an AP. also find $S_{20}$.
View full solution →Jaspal Singh repays his total loan of Rs. 118000 by paying every month starting with the first instalment of Rs. 1000. If he increases the instalment by Rs. 100 every month, what amount will be paid by him in the $30^{\text {th }}$ instalment? What amount of loan does he still have to pay after the $30^{\text {th }}$ instalment?
View full solution →Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to $\frac{\big(\text{a+c}\big)\big(\text{b + c - 2a}\big)}{2\big(\text{b - a}\big)}.$
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