Class 10 Maths · Chapter 5

Arithmetic Progressions

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

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 1 of 7

1. Q1 NCERT · Exercise 5.1
   In which of the following ​situations does the list of numbers involved make an arithmetic progression, and why? ​

   1. (i)The taxi fare after each km when the fare is Rs $15$ for the first km and Rs $8$ for each additional km.
   2. (ii)The amount of air present in ​a ​cylinder when a vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylinder at a time.
   3. (iii)The cost of digging a well after ​every metre of digging, when it costs Rs $150$ for the first metre and rises by Rs $50$ for each subsequent metre.
   4. (iv)The amount of money in ​the account every year, when Rs $10000$ is ​deposited at compound interest at $8\%$ per annum.
   Show answer

   (i) AP with $d=8$; (ii) Not an AP (air decreases by a constant factor $\frac{3}{4}$, so it is geometric); (iii) AP with $d=50$; (iv) Not an AP (balance grows by a constant factor $1.08$, so it is geometric).

   Step-by-step solution →
2. Q2 NCERT · Exercise 5.1
   Write the ​first four terms ​of ​the AP ​when the ​first term $a$ and the common difference $d$ are given as follows: ​

   1. (i)$a=10$, $d=10$
   2. (ii)$a=-2$, $d=0$
   3. (iii)$a=4$, $d=-3$ ​
   4. (iv)$a=-1$, $d=\frac{1}{2}$
   5. (v)$a=-1.25$, $d=-0.25$
   Show answer

   (i) $10,20,30,40$; (ii) $-2,-2,-2,-2$; (iii) $4,1,-2,-5$; (iv) $-1,-\frac{1}{2},0,\frac{1}{2}$; (v) $-1.25,-1.5,-1.75,-2.0$.

   Step-by-step solution →
3. Q3 NCERT · Exercise 5.1
   For the following ​APs, write ​the ​first ​term and ​the ​common difference: ​

   1. (i)$3,1,-1,-3,\dots$
   2. (ii)$-5,-1,3,7,\dots$
   3. (iii)$\frac{1}{3},\frac{5}{3},\frac{9}{3},\frac{13}{3},\dots$
   4. (iv)$0.6,1.7,2.8,3.9,\dots$
   Show answer

   (i) $a=3,d=-2$; (ii) $a=-5,d=4$; (iii) $a=\frac{1}{3},d=\frac{4}{3}$; (iv) $a=0.6,d=1.1$.

   Step-by-step solution →
4. Q4 NCERT · Exercise 5.1
   Which of the ​following ​are APs? If they ​form an AP, find the common difference $d$ and write ​three more terms. ​

   1. (i)$2,4,8,16,\dots$
   2. (ii)$2,\frac{5}{2},3,\frac{7}{2},\dots$
   3. (iii)$-1.2,-3.2,-5.2,-7.2,\dots$ ​
   4. (iv)$-10,-6,-2,2,\dots$
   5. (v)$3,3+\sqrt{2},3+2\sqrt{2},3+3\sqrt{2},\dots$
   6. (vi)$0.2,0.22,0.222,0.2222,\dots$
   7. (vii)$0,-4,-8,-12,\dots$
   8. (viii)$-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},\dots$
   Show answer

   APs: (ii) $d=\frac{1}{2}$; (iii) $d=-2$; (iv) $d=4$; (v) $d=\sqrt{2}$; (vii) $d=-4$; (viii) $d=0$. Not APs: (i) And (vi).

   Step-by-step solution →
5. Q5 NCERT · Exercise 5.2
   Fill in the ​blanks ​in the following ​table, given that $a$ is the first term, $d$ the ​common difference ​and $a_n$ the $n$-th term of the AP.

   1. (i)$a=7$, $d=3$, $n=8$, $a_n=?$
   2. (ii)$a=-18$, $d=?$, $n=10$, $a_n=0$
   3. (iii)$a=?$, $d=-3$, $n=18$, $a_n=-5$
   4. (iv)$a=-18.9$, $d=2.5$, $n=?$, $a_n=3.6$
   5. (v)$a=3.5$, $d=0$, $n=105$, $a_n=?$

   AP parameters with one missing value per row

   	$a$	$d$	$n$	$a_n$
   (i)	7	3	8	...
   (ii)	$-18$	...	10	0
   (iii)	...	$-3$	18	$-5$
   (iv)	$-18.9$	2.5	...	3.6
   (v)	3.5	0	105	...

   Show answer

   (i) $a_8=28$; (ii) $d=2$; (iii) $a=46$; (iv) $n=10$; (v) $a_{105}=3.5$.

   Step-by-step solution →
6. Q6 NCERT · Exercise 5.2
   Choose ​the correct choice in the following ​and justify:

   1. (i)30th term of the ​AP $10,7,4,\dots$ (A) 97 (B) 77 (C) $-77$ ​(D) $-87$
   2. (ii)11th ​term of ​the AP $-3,-\frac{1}{2},2,\dots$ (A) 28 (B) 22 (C) $-38$ (D) $-48\frac{1}{2}$
   Show answer

   (i) $a_{30}=-77$, option (C). (ii) $a_{11}=22$, option (B).

   Step-by-step solution →
7. Q7 NCERT · Exercise 5.2
   In the ​following APs, ​find ​the missing terms in the boxes: ​

   1. (i)$2,\square ,26$
   2. (ii)$\square ,13,\square ,3$
   3. (iii)$5,\square ,\square ,9\frac{1}{2}$ ​
   4. (iv)$-4,\square ,\square ,\square ,\square ,6$ ​
   5. (v)$\square ,38,\square ,\square ,\square ,-22$
   Show answer

   (i) $\square =14$; (ii) ${\square }_1=18,{\square }_2=8$; (iii) ${\square }_1=\frac{13}{2}=6.5,{\square }_2=8$; (iv) $-2,0,2,4$; (v) $53,23,8,-7$.

   Step-by-step solution →
8. Q8 NCERT · Exercise 5.2
   Which term of ​the ​AP: $3,8,13,18,\dots ,$ ​is ​78?
   Show answer

   $78$ is the $16$th term of the AP, so $n=16$.

   Step-by-step solution →
9. Q9 NCERT · Exercise 5.2
   Find the ​number ​of ​terms in each of the following ​APs:

   1. (i)$7,13,19,\dots ,205$ ​
   2. (ii)$18,15\frac{1}{2},13,\dots ,-47$
   Show answer

   (i) $n=34$; (ii) $n=27$.

   Step-by-step solution →
10. Q10 NCERT · Exercise 5.2
    Check whether $-150$ ​is ​a ​term ​of ​the AP: $11,8,5,2,\dots$
    Show answer

    No — solving gives $n=\frac{164}{3}$, which is not a whole number, so $-150$ is not a term of the AP.

    Step-by-step solution →
11. Q11 NCERT · Exercise 5.2
    Find the ​31st ​term ​of ​an AP whose 11th ​term is ​38 ​and the ​16th term is 73.
    Show answer

    The $31$st term of the AP is $178$.

    Step-by-step solution →
12. Q12 NCERT · Exercise 5.2
    An ​AP ​consists of 50 ​terms ​of which 3rd term ​is ​12 and the last term is 106. Find ​the 29th term.
    Show answer

    The $29$th term of the AP is $64$.

    Step-by-step solution →
13. Q13 NCERT · Exercise 5.2
    If the 3rd and the 9th ​terms of an ​AP ​are $4$ and $-8$ ​respectively, which term ​of ​this AP is zero?
    Show answer

    The $5$th term of the AP is zero.

    Step-by-step solution →
14. Q14 NCERT · Exercise 5.2
    The 17th term of an ​AP exceeds ​its 10th ​term by 7. Find ​the ​common ​difference.
    Show answer

    $d=1$.

    Step-by-step solution →
15. Q15 NCERT · Exercise 5.2
    Which ​term ​of ​the AP: $3,15,27,39,\dots$ ​will be 132 ​more than its 54th ​term?
    Show answer

    The $65$th term of the AP is $132$ more than its $54$th term.

    Step-by-step solution →
16. Q16 NCERT · Exercise 5.2
    Two APs have ​the same ​common ​difference. The difference between their ​100th terms ​is $100$. What is the ​difference ​between their 1000th terms?
    Show answer

    The difference between the $1000$th terms is also $100$.

    Step-by-step solution →
17. Q17 NCERT · Exercise 5.2
    How many ​three-digit ​numbers are ​divisible ​by 7?
    Show answer

    There are $128$ three-digit numbers divisible by $7$.

    Step-by-step solution →
18. Q18 NCERT · Exercise 5.2
    How ​many multiples ​of $4$ ​lie ​between $10$ and $250$?
    Show answer

    There are $60$ multiples of $4$ between $10$ and $250$.

    Step-by-step solution →
19. Q19 NCERT · Exercise 5.2
    For what ​value of $n$, are ​the $n$-th ​terms of two APs: $63,65,67,\dots$ ​and $3,10,17,\dots$ ​equal?
    Show answer

    The $13$th terms are equal, so $n=13$.

    Step-by-step solution →
20. Q20 NCERT · Exercise 5.2
    Determine ​the ​AP ​whose ​third term ​is $16$ ​and the $7$th ​term exceeds the $5$th term by $12$.
    Show answer

    The AP is $4,10,16,22,\dots$ (with $a=4$, $d=6$).

    Step-by-step solution →