CBSE Important Questions

Arithmetic Progression

23. A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes

24. For what value of 'K' the number 3K + 2, 4K +3 and 6K - 1 are the consecutive terms of an A.P.

25. Find the 12^th term from the end of the A.P. 3, 8, 13... 253.

26. The sum of three numbers in A.P. is 21 and their product is 231. Find the numbers,

27. Determine the AP whose 5^th term is 15 and the sum of its 3^rd and 8^th terms is 34.

28. Find the sum of all three digits numbers each of which leave the remainder 3 when divided by 5.

29. How many terms of the AP 78, 71, 64 . are needed to give the sum 468? Also, find the last terms of this AP.

30. If the sum of first nth terms of an AP is 3n²-2n. Find the AP and its 18^th terms.

31. Which terms of the AP 5, 15, 25 . . . will be 130 more than its 31th terms?

32. If the sum of 20^th terms of an AP is 1430. If the first term is 100. Find the last term and sum of 100^th terms.

33. Find the sum 3+ 11+ 19+ - - - +803.

34. If 7 times the 7^th term is to 11 times its 11th term of an AP then show that the 18^th terms of an AP is zero.

35. If pth terms of an AP is 1/q and qth term of AP is then show that the sum of pq terms is 1/2(pq+1).

36. How many terms in three digits numbers which is divisible by 7.

37. The first term, common difference and the last term of an AP are 12, 6 and 252 respectively. Find its sum.

38. Which term of an A.P 3, 10, 17..... will be 84 more than its 13^th term?

39. If the 10^th term of an A.P is 47 and first term is 2, find the sum of the first 15 terms.

40. In a given AP if pth term is q and the qth term is p, then show that the nth term is (p+q-n).

41. Find the sum of all three-digit natural numbers which are divisible by 13.

42. The sum of 'n' terms of the sequence is 3n²+4n. Find the n^th term and show that sequence of an A.P.

43. Find the value of m so that m+2, 4m-6 and 3m- 2 are three consecutive terms of an A

44. The sum of the third and the seventh terms of an A.P. are 6 and their product is 8. Find the sum of first 16 terms of the A.P.