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 11 of 23

1. Q201 CBSE 2024
   The $8^{\text{th}}$ term ​of ​an A.P., whose first ​two ​terms ​are $-5$ and $2$ respectively, ​is:

   1. (a)$-54$
   2. (b)$44$
   3. (c)$-61$
   4. (d)$-33$
   Show answer

   (b) $44$

   Step-by-step solution →
2. Q202 CBSE 2024
   The $30^{\text{th}}$ term of ​the ​AP $10,7,4,\dots$ ​is ​:

   1. (a)$87$
   2. (b)$77$
   3. (c)$-77$
   4. (d)$-87$
   Show answer

   (c) $-77$

   Step-by-step solution →
3. Q203 CBSE 2024
   The ​common difference ​of ​an A.P., ​if $a_{23}-a_{19}=32$, ​is ​:

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

   (a) 8

   Step-by-step solution →
4. Q204 CBSE 2024
   The $7^{th}$ ​term ​from ​the ​end ​of the A.P. ​: $-8,-5,-2,\dots ,49$ ​is :

   1. (a)$67$
   2. (b)$13$
   3. (c)$31$
   4. (d)$10$
   Show answer

   (c) $31$

   Step-by-step solution →
5. Q205 CBSE 2024
   The ​number ​of terms in ​the ​A.P. $3,6,9,12,\dots ,111$ is ​:

   1. (a)$36$
   2. (b)$40$
   3. (c)$37$
   4. (d)$30$
   Show answer

   (c) $37$

   Step-by-step solution →
6. Q206 CBSE 2024
   Three ​numbers in ​A.P. have ​the sum $30$. ​What is its ​middle ​term ​?

   1. (a)4
   2. (b)10
   3. (c)16
   4. (d)8
   Show answer

   (b) 10

   Step-by-step solution →
7. Q207 CBSE 2024
   Which term ​of the ​A.P. $-29,-26,-23,\dots ,61$ ​is $16$ ​?

   1. (a)$11^{th}$
   2. (b)$16^{th}$
   3. (c)$10^{th}$
   4. (d)$31^{st}$
   Show answer

   (b) $16^{th}$

   Step-by-step solution →
8. Q208 CBSE 2024
   The common ​difference ​of an ​A.P. ​whose $n^{th}$ ​term is given ​by $a_n=5n-1$, is :

   1. (a)$1$
   2. (b)$6$
   3. (c)$5$
   4. (d)$4$
   Show answer

   (c) $5$

   Step-by-step solution →
9. Q209 CBSE 2024
   $Assertion(A):$ ​Common difference ​of the A.P. $5,1,-3,-7,\dots$ is ​4. $Reason(R):$ ​Common difference of the A.P. $a_1,a_2,a_3,\dots ,a_n$ ​is obtained by $d=a_n-a_{n-1}$.

   Assertion (A): Common difference of the A.P. 5, 1, -3, -7, ... is 4.

   Reason (R): Common difference of the A.P. a1, a2, a3, ..., an is obtained by d = an - a(n-1).

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true, but Reason (R) is false.
   4. (d)Assertion (A) is false, but Reason (R) is true.
   Show answer

   (d) Assertion (A) is false, but Reason (R) is true.

   Step-by-step solution →
10. Q210 CBSE 2024
    Directions: A statement of ​Assertion ​(A) ​is ​followed ​by ​a statement of ​Reason (R). Choose the correct ​option.

    Assertion (A): The eighth term of the A.P. $\frac{1}{m},\frac{1+2m}{m},\frac{1+4m}{m},\dots$ is $\frac{1+14m}{m}$.

    Reason (R): The $n^{th}$ term of A.P. $(a_n)=a+(n-1)d$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

    Step-by-step solution →
11. Q211 CBSE 2024
    Two statements ​are ​given - ​one labelled Assertion (A) and the other labelled Reason (R). Select the ​correct ​option.

    Assertion (A): The sum of the first fifteen terms of the AP 21, 18, 15, 12, ... is zero.

    Reason (R): The sum of the first n terms of an AP with first term 'a' and common difference 'd' is given by $S_n=\frac{n}{2}[a+(n-1)d]$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (c) Assertion (A) is true, but Reason (R) is false.

    Step-by-step solution →
12. Q212 CBSE 2024
    If the ​sum of ​first $m$ terms of an ​A.P. ​is same as sum ​of its first $n$ ​terms $(m\ne n)$, then show ​that the sum of its first $(m+n)$ ​terms is zero.
    Show answer

    From $S_m=S_n$ and $m\ne n$ we get $2a+(m+n-1)d=0$, so $S_{m+n}=\frac{m+n}{2}[2a+(m+n-1)d]=\frac{m+n}{2}\times 0=0$. Hence proved.

    Step-by-step solution →
13. Q213 CBSE 2024
    If the ​sum ​of first $7$ ​terms of an A.P. is $49$ and that ​of first $17$ ​terms is $289$, find the sum of ​its first $20$ terms.
    Show answer

    The sum of the first $20$ terms is $S_{20}=400$.

    Step-by-step solution →
14. Q214 CBSE 2024
    The ratio ​of the $10^{\text{th}}$ ​term to its $30^{\text{th}}$ ​term of an A.P. ​is $1:3$ and ​the sum of its first six terms is $42$. Find the first term and the common difference ​of A.P.
    Show answer

    The first term is $a=2$ and the common difference is $d=2$ (the A.P. is $2,4,6,8,\dots$).

    Step-by-step solution →
15. Q215 CBSE 2024
    In an A.P., ​the ​sum of three consecutive terms is $24$ and the ​sum of their ​squares is $194$. ​Find ​the ​numbers.
    Show answer

    The numbers are $7$, $8$ and $9$ (for $d=1$ they are $7,8,9$; for $d=-1$ the same numbers in the order $9,8,7$).

    Step-by-step solution →
16. Q216 CBSE 2024
    If the sum of the first $14$ ​terms of ​an A.P. is $1050$ and the first ​term is $10$, then ​find the $20^{\text{th}}$ ​term and ​the $n^{\text{th}}$ ​term.
    Show answer

    The common difference is $d=10$, so the $20^{\text{th}}$ term is $a_{20}=200$ and the $n^{\text{th}}$ term is $a_n=10n$.

    Step-by-step solution →
17. Q217 CBSE 2024
    The first term of an A.P. is $5$, the ​last term is $45$ and the ​sum of all the terms is $400$. ​Find the ​number ​of terms and the common difference ​of the ​A.P.
    Show answer

    Number of terms $n=16$; common difference $d=\frac{8}{3}$.

    Step-by-step solution →
18. Q218 CBSE 2024
    How ​many ​terms of the ​A.P. $27,24,21,\dots$ must be taken so ​that ​their ​sum is $105$? Which term of the A.P. is ​zero?
    Show answer

    $5$ terms or $14$ terms must be taken to get the sum $105$; the $10$th term of the A.P. is zero.

    Step-by-step solution →
19. Q219 CBSE 2024
    Find the sum ​of ​all ​integers ​between $50$ and $500$ ​which are divisible ​by $7$.
    Show answer

    The sum of all integers between $50$ and $500$ that are divisible by $7$ is $17696$.

    Step-by-step solution →
20. Q220 CBSE 2024
    The ​sum of ​first and eighth terms of an A.P. is $32$ ​and their product ​is $60$. Find the first term and common difference of ​the ​A.P. Hence, also find the sum ​of its first $20$ terms.
    Show answer

    Either $a=2$, $d=4$ and $S_{20}=800$, or $a=30$, $d=-4$ and $S_{20}=-160$.

    Step-by-step solution →