Class 10 Maths · Chapter 5

Arithmetic Progressions

441 Class 10 Maths questions on Arithmetic Progressions from the NCERT textbook, NCERT Exemplar and CBSE board papers 2015–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 7 of 23

1. Q121 CBSE 2026
   The $31^{\text{st}}$ ​term ​of ​the ​A.P. : $\frac{-5}{6},\frac{-3}{4},\frac{-2}{3},\frac{-7}{12},\dots$ is

   1. (a)$\frac{-5}{3}$
   2. (b)$\frac{5}{3}$
   3. (c)$\frac{12}{20}$
   4. (d)$\frac{-12}{20}$
   Show answer

   (b) $\frac{5}{3}$

   Step-by-step solution →
2. Q122 CBSE 2026
   The $n^{\text{th}}$ ​term of an ​A.P. ​is $3n+2$. The ​common ​difference ​is:

   1. (a)$8$
   2. (b)$2$
   3. (c)$5$
   4. (d)$3$
   Show answer

   (d) $3$

   Step-by-step solution →
3. Q123 CBSE 2026
   The common ​difference of the ​AP ​: $\sqrt{2},2\sqrt{2},3\sqrt{2},4\sqrt{2},\dots$ ​is ​:

   1. (a)$\sqrt{2}$
   2. (b)$1$
   3. (c)$2\sqrt{2}$
   4. (d)$-\sqrt{2}$
   Show answer

   (a) $\sqrt{2}$

   Step-by-step solution →
4. Q124 CBSE 2026
   The ​number of ​multiples ​of $4$ ​lying ​between $12$ ​and $250$ is ​:

   1. (a)$59$
   2. (b)$59.5$
   3. (c)$60$
   4. (d)$61$
   Show answer

   (a) $59$

   Step-by-step solution →
5. Q125 CBSE 2026
   Which ​of ​the ​following ​sequence ​is ​not ​an A.P. ?

   1. (a)$2,\frac{5}{2},3,\frac{7}{2},\dots$
   2. (b)$-1.2,-3.2,-5.2,-7.2,\dots$
   3. (c)$\sqrt{2},\sqrt{8},\sqrt{18},\dots$
   4. (d)$1^2,3^2,5^2,7^2,\dots$
   Show answer

   (d) $1^2,3^2,5^2,7^2,\dots$

   Step-by-step solution →
6. Q126 CBSE 2026
   The sum of ​first $n$ terms of an A.P. ​is $50\sqrt{2}$. If the first ​and ​the ​last terms are $\sqrt{2}$ and $19\sqrt{2}$ respectively, then ​the value of $n$ ​is:

   1. (a)$10$
   2. (b)$5$
   3. (c)$15$
   4. (d)$20$
   Show answer

   (b) $5$

   Step-by-step solution →
7. Q127 CBSE 2026
   If $a_n$ ​represents the $n^{\text{th}}$ ​term ​of the ​A.P. $-\frac{15}{4},-\frac{10}{4},-\frac{5}{4},\dots$ then ​the ​value ​of $a_{16}-a_{12}$ is :

   1. (a)$4$
   2. (b)$\frac{5}{4}$
   3. (c)$5$
   4. (d)$\frac{25}{4}$
   Show answer

   (c) $5$

   Step-by-step solution →
8. Q128 CBSE 2026
   If the mean of ​first $n$ ​natural numbers is $\frac{6n}{11}$, ​then $n$ ​is :

   1. (a)$11$
   2. (b)$6$
   3. (c)$12$
   4. (d)$22$
   Show answer

   (a) $11$

   Step-by-step solution →
9. Q129 CBSE 2026
   $n^{\text{th}}$ ​term ​of the A.P. ​: $\frac{-1}{3},\frac{4}{3},3,\dots$ ​is

   1. (a)$\frac{5n-9}{3}$
   2. (b)$\frac{5n-6}{3}$
   3. (c)$\frac{3n-4}{3}$
   4. (d)$\frac{3n+2}{3}$
   Show answer

   (b) $\frac{5n-6}{3}$

   Step-by-step solution →
10. Q130 CBSE 2026
    If $a$, $b$, $c$ ​and $d$ are ​consecutive ​terms ​of ​an A.P., then $c-b$ ​is equal to:

    1. (a)$d-a$
    2. (b)$d-b$
    3. (c)$d-c$
    4. (d)$c-a$
    Show answer

    (c) $d-c$

    Step-by-step solution →
11. Q131 CBSE 2026
    The $n^{\text{th}}$ ​term of ​the ​A.P. $\frac{-1}{3},\frac{2}{3},\frac{5}{3},\frac{8}{3},\dots$ ​is :

    1. (a)$3n-4$
    2. (b)$n-\frac{4}{3}$
    3. (c)$\frac{n-2}{3}$
    4. (d)$\frac{n-4}{3}$
    Show answer

    (b) $n-\frac{4}{3}$

    Step-by-step solution →
12. Q132 CBSE 2026
    The $10^{\text{th}}$ term ​of the A.P. $\sqrt{2},\sqrt{8},\sqrt{18},\dots$ ​is ​:

    1. (a)$\sqrt{162}$
    2. (b)$\sqrt{200}$
    3. (c)$\sqrt{54}$
    4. (d)$\sqrt{94}$
    Show answer

    (b) $\sqrt{200}$

    Step-by-step solution →
13. Q133 CBSE 2026
    If $a$, $b$ ​and $c$ ​are ​in ​A.P., ​then ​:

    1. (a)$2a$, $3b$ and $4c$ are also in A.P.
    2. (b)$a-2$, $b-2$ and $c-2$ are also in A.P.
    3. (c)$\frac{a}{2}$, $\frac{b}{3}$ and $\frac{c}{4}$ are also in A.P.
    4. (d)$a+2$, $b+3$ and $c+4$ are also in A.P.
    Show answer

    (b) $a-2$, $b-2$ and $c-2$ are also in A.P.

    Step-by-step solution →
14. Q134 CBSE 2026
    The ​numbers $x,x+4$ ​and $x+8$ are in ​A.P. ​with ​common difference :

    1. (a)$x$
    2. (b)$4+x$
    3. (c)$4$
    4. (d)$0$
    Show answer

    (c) $4$

    Step-by-step solution →
15. Q135 CBSE 2026
    If $-26,x,2$ ​are in ​A.P., then the ​value ​of $x$ ​is

    1. (a)$14$
    2. (b)$-13$
    3. (c)$-12$
    4. (d)$-14$
    Show answer

    (c) $-12$

    Step-by-step solution →
16. Q136 CBSE 2026
    $n^{\text{th}}$ ​term of the A.P. $-\frac{3}{2},\frac{3}{2},\frac{9}{2},\dots$ ​is ​:

    1. (a)$\frac{3n}{2}-3$
    2. (b)$3n-\frac{9}{2}$
    3. (c)$\frac{3n-9}{2}$
    4. (d)$3n+\frac{3}{2}$
    Show answer

    (b) $3n-\frac{9}{2}$

    Step-by-step solution →
17. Q137 CBSE 2026
    In an A.P., the ​first ​term ​is $32$ ​and the last term is $-10$. If the ​common difference is $-2$, ​then find the number of terms ​and their ​sum.
    Show answer

    The number of terms is $22$ and their sum is $242$.

    Step-by-step solution →
18. Q138 CBSE 2026
    Find ​the sum of the ​first $28$ ​terms ​of ​an ​A.P. whose $n^{\text{th}}$ term is ​given ​by $a_n=3n-2$.
    Show answer

    The sum of the first $28$ terms is $S_{28}=1162$.

    Step-by-step solution →
19. Q139 CBSE 2026
    The ​sum of first $n$ ​terms of an A.P. ​is ​given by $S_n=4n^2-n$. ​Find ​the $25^{\text{th}}$ term of this ​A.P.
    Show answer

    The $25^{\text{th}}$ term is $a_{25}=195$.

    Step-by-step solution →
20. Q140 CBSE 2026
    In an ​A.P., the $15^{\text{th}}$ term ​exceeds the $8^{\text{th}}$ term by $21$. ​If the ​sum of the first $10$ ​terms ​is $55$, then form the A.P.
    Show answer

    The A.P. has first term $a=-8$ and common difference $d=3$, so it is $-8,-5,-2,1,4,\dots$

    Step-by-step solution →