Gyaankosh has provided the Important 2025 CBSE Questions from the chapter – Arithmetic Progressions of Class 10th mainly for students appearing for CBSE 2025 exams. This Arithmetic progressions is the important chapter among the other chapters of Class 10th which is helpful for scoring in the final CBSE exams.

We have analyzed various Maths reference books and Maths NCERT book and filtered some important questions for CBSE 2025 exam for chapter Arithmetic Progressions. Check out the questions below –

Important Arithmetic Progressions Questions

Q1. An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find the 32^nd term. [NCERT Exemplar]

Ans. 69

Q2. The 26^th, 11^th and last term of an A.P. are 0, 3 and -1/5 respectively. Find the common difference and the number of terms.

Ans. d = -1/5 and n = 27

Q3. How many numbers of two digit are divisible by 3?

Ans. 30

Q4. The 4^th term of an A.P. is three times the first and the 7^th term exceeds twice the third term by 1. Find the first term and the common difference.

Ans. First term = 3 and Common Difference = 2

Q5. The sum of the 4^th and 8^th terms of an A.P. is 24 and the sum of the 6^th and 10^th terms is 34. Find the first term and the common difference of the A.P.

Ans. First term = -1/2 and Common Difference = 5/2

Q6. In which of the following situations, the sequence of numbers formed will form an A.P.? [Imp]

1. Divya deposited Rs.1000 at compound interest at the rate of 10% per annum. The amount at the end of first year, second year, third year,……….. and so on.
   
   Ans. No
   
2. The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 20 for each succeeding metre.
   
   Ans. Yes

Q7. The n^th term of an A.P. is 6n+2. Find the common difference. [CBSE 2008]

Ans. 6

Q8. The general term of a sequence is given by a_n = -4n+15. Is the sequence an A.P.? If so, find its 15th term and the common difference. [Imp]

Ans. 15th term = -45 and Common Difference = – 4

Q9. Consider the A.P. 2, 5, 8, 11, ……,302. Show that twice of the middle term of the above A.P. is equal to the sum of its first and the last term.

Q10. If the 8^th term of an A.P. is 31 and the 15^th term is 16 more than the 11^th term, find the A.P. [CBSE 2006]

Ans. A.P. is a, a+d, a+2d, a+3d,…… i.e. 3, 7, 11, 15, 19,……

Q11. If the m^th term of an A.P. be 1/n and n^th term be 1/m, then show that its (mn)^th term is 1. [CBSE 2017]

Q12. If the p^th term of an A.P. is q and the q^th term is p, prove that its n^th term is (p+q-n). [CBSE 2008, 2017]

Q13. If m times the m^th term of an A.P. is equal to n times its n^th term, show that the (m+n)^th term of an A.P. is zero. [CBSE 2008, 2019]

Q14. If p^th, q^th and r^th terms of an A.P. are a, b, c respectively, then show that – [CBSE 2008, 2019]

i) a (q-r) + b (r-p) + c (p-q) = 0

ii) (a-b) r + (b-c) p + (c-a) q = 0

Q15. If the n^th term of an A.P. 9, 7, 5,….. is same as the n^th term of the A.P. 15, 12, 9…… Find the n.

Ans. 7

Q16. The 6^th and 17^th terms of an A.P. are 19 and 41 respectively, find the 40^th term.

Ans. 87

Q18. If the 9^th term of an A.P. is Zero, then prove that its 29^th term is double the 19^th term.

Q19. In a certain A.P, the 24^th term is twice the 10^th term. Prove that the 72^nd term is twice the 34^th term.

Q20. Which term of an A.P. 5, 15, 25,…….. will be 130 more than its 31^st term? [CBSE 2006, 2017]

Ans. n = 44

Q21. The 7^th term of an A.P. is 32 and the 13^th term is 62. Find the A.P. [CBSE 2004]

Ans. A.P. is 2, 7, 12, 17,……

Q22. How many multiples of 4 lie between 10 and 250? [NCERT]

Ans. 60

Q23. How many three digits numbers are divisible by 7? [CBSE 2013]

Ans. 128

Q24. Find the 8^th term from the end of the A.P. 7, 10, 13,………, 184. [CBSE 2005]

Ans. 163

Q25. Find the term of the Arithmetic Progressions 9, 12, 15, 18,……… which is 39 more than its 36^th term? [CBSE 2006C]

Ans. 49^th

Q26. The 17^th term of an A.P. is 5 more than twice its 8^th term. If the 11^th term of the A.P. is 43, find the n^th term. [CBSE 2012]

Ans. 4n-1

Q27. The 19^th term of an A.P. is equal to three times its sixth term. If the 9^th term is 19, find the A.P. [CBSE 2013]

Ans. 3, 5, 7, 9,…….

Q28. The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P. [CBSE 2014]

Ans. 3, 5, 7, 9, 11,…….

Q29. Find whether 0 (zero) is a term of the A.P. 40, 37, 34, 31,……. [CBSE 2014]

Ans. No

Q30. Find the middle term of an A.P. 213, 205, 197,……., 37. [CBSE 2015]

Ans. 125

Q31. How many numbers lie between 10 and 300 which when divided by 4 leave a remainder 3? [NCERT Exemplar]

Ans. 73

Q32. Find the four numbers in A.P. whose sum is 20 and sum of whose squares is 120.

Ans. 2, 4, 6, 8 or 8, 6, 4, 2.

Q33. The sum of the first three terms of an A.P. is 33. If the product of first and the third term exceeds the second term by 29, find the A.P. [NCERT Exemplar]

Ans. Two A.P.’s are there 2, 11, 20, 29, ……. and 20, 11, 2, ……..

Q34. The sum of three numbers in an A.P. is 12 and the sum of their cubes is 288. Find the numbers. [CBSE 2016]

Ans. 2,4,6 and 6,4,2.

Q35. Divide 56 in four parts in A.P. such that the ratio of the product of their extremes to the product of their means is 5:6. [CBSE 2016]

Ans. 8, 12, 16, 20.

Q36. The angles of a quadrilateral are in A.P. whose common difference is 10^o. Find the angles. [CBSE 2016]

Ans. 75^o, 85^o, 95^o, 105^o.

Q37. If the n^th term of an A.P. is (2n+1), find the sum of first n terms of the A.P. [CBSE 2005]

Ans. S_n = n (n+2)

Q38. Find the sum of first 20 terms of an A.P. in which 3^rd term is 7 and 7^th term is two more than thrice of its third term.

Ans. 740

Q39. Find the sum of all three digit natural numbers which are divisible by 7. [CBSE 2006C]

Ans. 70336

Q40. The sum of first six terms of an A.P. is 42. The ratio of its 10th term to its 30th term is 1:3. Find the first and the 13^th term of an A.P. [CBSE 2009]

Ans. a = 2 and a₁₃ = 26

Q41. If the ratio 11^th term of an A.P. to its 18^th term is 2:3, find the ratio of the sum of first five terms to the sum of its first 10 terms. [CBSE 2017]

Ans. 6:17

Q42. If S_n, the sum of first n terms of an A.P. is given by S_n = 5n²+3n, then find its n^th term. [CBSE 2009]

Ans. 10n-2

Q43. In an A.P., the sum of first n terms is 3n²/2 + 5n/2. Find its 25th term. [CBSE 2006C]

Ans. 76

Q44. Find the sum of all 11 terms of an A.P. whose middle most term is 30. [NCERT Exemplar]

Ans. 330

Q45. If the m^th term of an A.P. is 1/n and n^th term of an A.P. is 1/m, show that the sum of mn terms is 1/2(mn+1). [CBSE 2015, 2017]