Mastering Arithmetic Progressions: A Class 10 NCERT Practice Quiz

Question 1

Which of the following is an Arithmetic Progression?

Accepted Answer

$-10, -6, -2, 2, \dots$

Answer

$1, 3, 6, 10, \dots$

Answer

$2, 4, 8, 16, \dots$

Answer

$1/2, 1/3, 1/4, 1/5, \dots$

Question 2

What is the common difference of the AP: $1/3, 5/3, 9/3, 13/3, \dots$?

Accepted Answer

$4/3$

Answer

$1/3$

Answer

$2/3$

Answer

$1$

Question 3

The $n^{	ext{th}}$ term of an AP is given by $a_n = 3 + 4n$. The common difference is:

Accepted Answer

$4$

Answer

$3$

Answer

$7$

Answer

$1$

Question 4

If the first term of an AP is $5$ and the common difference is $3$, find the $10^{	ext{th}}$ term.

Accepted Answer

$32$

Answer

$35$

Answer

$38$

Answer

$41$

Question 5

Which term of the AP $21, 18, 15, \dots$ is $-81$?

Accepted Answer

$35^{	ext{th}}$

Answer

$34^{	ext{th}}$

Answer

$36^{	ext{th}}$

Answer

$37^{	ext{th}}$

Question 6

How many two-digit numbers are divisible by $3$?

Accepted Answer

$30$

Answer

$29$

Answer

$31$

Answer

$32$

Question 7

Find the sum of the first $20$ terms of the AP: $1, 4, 7, 10, \dots$.

Accepted Answer

$600$

Answer

$590$

Answer

$610$

Answer

$620$

Question 8

The $17^{	ext{th}}$ term of an AP exceeds its $10^{	ext{th}}$ term by $7$. The common difference is:

Accepted Answer

$1$

Answer

$2$

Answer

$3$

Answer

$4$

Question 9

If $x+1, 3x, 4x+2$ are in AP, find the value of $x$.

Accepted Answer

$3$

Answer

$1$

Answer

$2$

Answer

$4$

Question 10

The sum of the first $15$ multiples of $8$ is:

Accepted Answer

$960$

Answer

$920$

Answer

$940$

Answer

$980$

Question 11

The sum of the first $n$ terms of an AP is $S_n = 2n^2 + 5n$. Find its $n^{	ext{th}}$ term.

Accepted Answer

$4n+3$

Answer

$4n+7$

Answer

$4n+5$

Answer

$2n+7$

Question 12

If the sum of the first $7$ terms of an AP is $49$ and that of $17$ terms is $289$, find the sum of the first $n$ terms.

Accepted Answer

$n^2$

Answer

$2n^2$

Answer

$n(n+1)/2$

Answer

$n(n-1)$

Question 13

If the $m^{	ext{th}}$ term of an AP is $1/n$ and the $n^{	ext{th}}$ term is $1/m$, then its $(mn)^{	ext{th}}$ term is:

Accepted Answer

$1$

Answer

$0$

Answer

$mn$

Answer

$1/(mn)$

Question 14

The sum of all natural numbers between $100$ and $200$ which are divisible by $6$ is:

Accepted Answer

$2550$

Answer

$2400$

Answer

$2450$

Answer

$2500$

Question 15

If the $p^{	ext{th}}$ term of an AP is $q$ and the $q^{	ext{th}}$ term is $p$, then the $r^{	ext{th}}$ term is:

Accepted Answer

$p+q-r$

Answer

$p+q+r$

Answer

$p-q+r$

Answer

$p-q-r$

Question 16

The sum of first $n$ odd natural numbers is:

Accepted Answer

$n^2$

Answer

$n$

Answer

$n+1$

Answer

$n(n+1)$

Question 17

If the $2^{	ext{nd}}$ term of an AP is $13$ and the $5^{	ext{th}}$ term is $25$, what is the $10^{	ext{th}}$ term?

Accepted Answer

$45$

Answer

$41$

Answer

$49$

Answer

$53$

Question 18

The list of numbers $-10, -8, -6, -4, \dots$ has $20$ terms. What is the last term?

Accepted Answer

$28$

Answer

$30$

Answer

$32$

Answer

$34$

Question 19

In an AP, if $a=3.5, d=0, n=101$, then $a_n$ will be:

Accepted Answer

$3.5$

Answer

$0$

Answer

$101$

Answer

$104.5$

Question 20

If $a_n = 3 - 2n$, then the common difference is:

Accepted Answer

$-2$

Answer

$2$

Answer

$3$

Answer

$-3$

Question 21

How many terms are there in the AP whose first term is $3$, common difference is $4$ and the last term is $43$?

Accepted Answer

$11$

Answer

$10$

Answer

$12$

Answer

$13$

Question 22

The sum of the first $n$ terms of an AP is $3n^2 - n$. What is its $3^{	ext{rd}}$ term?

Accepted Answer

$16$

Answer

$14$

Answer

$18$

Answer

$20$

Question 23

For an AP, $a_k = 2k+1$. What is the sum of its first three terms?

Accepted Answer

$15$

Answer

$12$

Answer

$18$

Answer

$21$

Question 24

A sum of Rs. $1000$ is invested at $8\%$ simple interest per year. Calculate the interest at the end of $30$ years. Is it an AP? If so, find the amount of interest.

Accepted Answer

AP, Rs. $2400$

Answer

Not an AP

Answer

AP, Rs. $240$

Answer

AP, Rs. $80$

Question 25

The $4^{	ext{th}}$ term from the end of the AP $-11, -8, -5, \dots, 49$ is:

Accepted Answer

$40$

Answer

$37$

Answer

$34$

Answer

$31$

Question 26

If the $9^{	ext{th}}$ term of an AP is zero, then its $29^{	ext{th}}$ term is how many times its $19^{	ext{th}}$ term?

Accepted Answer

$2$

Answer

$1$

Answer

$3$

Answer

$4$

Question 27

In an AP, if $d=-4, n=7, a_n=4$, then $a$ is:

Accepted Answer

$28$

Answer

$6$

Answer

$7$

Answer

$20$

Question 28

The sum of the first $n$ terms of an AP is $5n - n^2$. What is the common difference?

Accepted Answer

$-2$

Answer

$2$

Answer

$4$

Answer

$-4$

Question 29

If $a, b, c$ are in AP, then $(a-c)^2 / (b^2-ac)$ is equal to:

Accepted Answer

$4$

Answer

$1$

Answer

$2$

Answer

$3$

Question 30

The sum of the first $100$ terms of an AP with $a_1=2$ and $a_{100}=200$ is:

Accepted Answer

$10100$

Answer

$10000$

Answer

$9900$

Answer

$20200$

Questions in this Quiz

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Mastering Arithmetic Progressions: A Class 10 NCERT Practice Quiz

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