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 9 of 23

1. Q161 CBSE 2025
   The $8^{th}$ ​term ​from ​the ​end ​of the A.P. $3,7,11,15,\dots ,143$ ​is

   1. (a)$135$
   2. (b)$125$
   3. (c)$115$
   4. (d)$111$
   Show answer

   (c) $115$

   Step-by-step solution →
2. Q162 CBSE 2025
   The 20th ​term ​of ​the ​A.P. $10\sqrt{2},6\sqrt{2},2\sqrt{2},\dots$ ​is ​:

   1. (a)$-76+10\sqrt{2}$
   2. (b)$-62\sqrt{2}$
   3. (c)$-66\sqrt{2}$
   4. (d)$86\sqrt{2}$
   Show answer

   (c) $-66\sqrt{2}$

   Step-by-step solution →
3. Q163 CBSE 2025
   The $5^{th}$ ​term ​from the ​end of an ​AP $-11,-8,-5,\dots ,55$ ​is:

   1. (a)$1$
   2. (b)$43$
   3. (c)$40$
   4. (d)$46$
   Show answer

   (b) $43$

   Step-by-step solution →
4. Q164 CBSE 2025
   If the sum ​of ​first $m$ terms of an AP ​is $2m^2+3m$, ​then its second term ​is :

   1. (a)$10$
   2. (b)$9$
   3. (c)$12$
   4. (d)$4$
   Show answer

   (b) $9$

   Step-by-step solution →
5. Q165 CBSE 2025
   If the ​sum of the ​first $n$ ​terms of an AP ​is $2n^2+5n$, ​then its common difference ​is :

   1. (a)2
   2. (b)4
   3. (c)5
   4. (d)7
   Show answer

   (b) 4

   Step-by-step solution →
6. Q166 CBSE 2025
   The $10^{\text{th}}$ ​term of ​the ​AP $5,\frac{19}{4},\frac{9}{2},\frac{17}{4},\dots$ ​is ​:

   1. (a)$\frac{11}{4}$
   2. (b)$\frac{4}{11}$
   3. (c)$\frac{13}{4}$
   4. (d)$\frac{4}{13}$
   Show answer

   (a) $\frac{11}{4}$

   Step-by-step solution →
7. Q167 CBSE 2025
   If ​the sum of first n terms of an A.P. ​is ​given by $S_n=\frac{n}{2}(3n+1)$, ​then ​the ​first term of the ​A.P. ​is

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

   (a) $2$

   Step-by-step solution →
8. Q168 CBSE 2025
   The ​next term of the ​A.P. $\sqrt{5},\sqrt{20},\sqrt{45},\dots$ ​is ​:

   1. (a)$\sqrt{60}$
   2. (b)$4\sqrt{5}$
   3. (c)$\sqrt{75}$
   4. (d)$\sqrt{125}$
   Show answer

   (b) $4\sqrt{5}$

   Step-by-step solution →
9. Q169 CBSE 2025
   Read the ​Assertion (A) ​and Reason ​(R) ​and choose ​the correct ​option.

   Assertion (A): Common difference of the AP $5,1,-3,-7,\dots$ is $4$.

   Reason (R): Common difference of the AP $a_1,a_2,a_3,\dots ,a_n$ is obtained by $d=a_n-a_{n-1}$.

   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. Q170 CBSE 2025
    Choose ​the ​correct option (a)-(d) based on the truth ​values ​of the ​Assertion ​(A) ​and Reason ​(R) below.

    Assertion (A): For an A.P., $3,6,9,\dots ,198$, $10^{\text{th}}$ term from the end is $168$.

    Reason (R): If $a$ and $l$ are the first term and last term of an A.P. with common difference $d$, then $n^{th}$ term from the end of the given A.P. is $l-(n-1)d$.

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

    (d) A is false but R is true.

    Step-by-step solution →
11. Q171 CBSE 2025
    Find ​the sum of ​the ​A.P. $7,10.5,14,\dots ,84$.
    Show answer

    The sum of the A.P. is $S_{23}=\frac{2093}{2}=1046.5$.

    Step-by-step solution →
12. Q172 CBSE 2025
    If the sum of ​first $n$ ​terms of an ​A.P. is given by $S_n=\frac{n}{2}(2n+8)$, then ​find ​its first term and common difference. Hence, find ​its 15th term.
    Show answer

    First term $a=5$, common difference $d=2$, and the 15th term $a_{15}=33$.

    Step-by-step solution →
13. Q173 CBSE 2025
    Find ​the ​middle ​term(s) ​of ​the ​A.P. $9,15,21,\dots ,243$.
    Show answer

    The A.P. has $40$ terms, so it has two middle terms: the $20$th term, $123$, and the $21$st term, $129$.

    Step-by-step solution →
14. Q174 CBSE 2025
    The ​sum ​of ​the third and seventh ​terms of an ​AP is $40$ and the ​sum of its sixth ​and fourteenth terms is $70$. Find the sum of the first ten terms of ​the AP.
    Show answer

    The sum of the first ten terms is $S_{10}=215$ (with first term $a=8$ and common difference $d=3$).

    Step-by-step solution →
15. Q175 CBSE 2025
    A sum ​of Rs. $2,000$ ​is invested at $7\%$ per ​annum simple interest. Calculate the interests at the end ​of $1^{\text{st}},2^{\text{nd}}$ and $3^{\text{rd}}$ year. Do these interests ​form ​an AP? ​If so, ​find the interest at the end of the $27^{\text{th}}$ year.
    Show answer

    The interests at the end of the 1st, 2nd and 3rd years are ₹140, ₹280 and ₹420; they form an AP with $a=140$ and $d=140$, and the interest at the end of the 27th year is ₹3780.

    Step-by-step solution →
16. Q176 CBSE 2025
    Find ​the ​A.P. whose third term is $16$ and seventh ​term exceeds the fifth term ​by $12$. Also, ​find ​the sum ​of first $29$ terms of the ​A.P.
    Show answer

    The A.P. is $4,10,16,22,\dots$ (first term $a=4$, common difference $d=6$), and the sum of its first $29$ terms is $S_{29}=2552$.

    Step-by-step solution →
17. Q177 CBSE 2025
    Find the sum of the first $20$ ​terms of an A.P. ​whose $n^{\text{th}}$ term is ​given ​by $a_n=5+2n$. Can $52$ ​be a ​term of ​this A.P.?
    Show answer

    The sum of the first $20$ terms is $S_{20}=520$. No, $52$ is not a term of this A.P.: $5+2n=52$ gives $n=\frac{47}{2}$, which is not a natural number.

    Step-by-step solution →
18. Q178 CBSE 2025
    The ​sum of the ​third term ​and the seventh term of ​an AP is $6$ ​and ​their product ​is $8$. Find the sum of ​the first sixteen terms of the AP.
    Show answer

    The sum of the first sixteen terms is $76$ (when $a=1$, $d=\frac{1}{2}$) or $20$ (when $a=5$, $d=-\frac{1}{2}$).

    Step-by-step solution →
19. Q179 CBSE 2025
    The ​minimum age of children eligible to participate in a painting competition is $8$ years. It is observed that the age of the youngest boy ​was $8$ ​years and the ages of the participants, when seated in order of age, have a common ​difference of $4$ ​months. If the sum ​of ​the ages of all the participants is $168$ years, find the age of the eldest participant in the ​painting competition.
    Show answer

    The eldest participant in the painting competition is $13$ years old.

    Step-by-step solution →
20. Q180 CBSE 2025
    Case ​Study - 1: In ​a society, a yoga instructor was hired to train the people of the society to live a healthy lifestyle. Yoga sessions were held daily from 5 p.m. to 7 p.m. in the society park. On day one, 5 people joined the yoga ​session, on day ​two, ​3 more ​people joined, on day three, another 3 people joined and in this manner every ​next day, 3 more people kept on joining. Based on the given information, answer the following questions:

    1. iOn which day did $59$ people join the yoga session?[1]
    2. iiHow many people joined the yoga session on the $31$st day?[1]
    3. iii(a)The yoga instructor was paid $\text{₹}100$ for each person attending the yoga session. On which day would he earn $\text{₹}5,000$?[2]
    4. iii(b)What was the total amount earned by the yoga instructor in $16$ days?[2]
    Show answer

    (i) The 19th day; (ii) $95$ people; (iii)(a) The 16th day; (iii)(b) ₹44,000.

    Step-by-step solution →