**IIT Foundation Mathematics Problems** are helpful for students aspiring for NTSE, Olympiad, KVPY, IIT JEE and other engineering and competitive exams. These questions are prepared by best faculties from all over India.

Here we are providing problems on ** Sequence and Series** based on topic

**.**

*Arithmetic Progression***Q.1. **Find the 26th term of the A.P: 10, 6, 2, –2, – 6, –10, ….. ?

(a) –86

(b) 96

(c) –90

(d) –106

## Answer

Answer: c**Q.2. **If p times the p^{th} term of an A.P. is q times the q^{th} term, then what is (p + q)^{th} term equal to?

(a) p + q

(b) pq

(c) 1

(d) 0

## Answer

Answer: d**Q.3.** The 59th term of an A.P. is 449 and the 449th term is 59. Which term is equal to 0?

(a) 501^{st }term

(b) 502^{nd} term

(c) 508^{th} term

(d) 509^{th }term

## Answer

Answer: c**Q.4.** If a, b, c be in Arithmetic Progression, then the value of (a + 2b – c) (2b + c – a) (a + 2b + c) is

(a) 3abc

(b) 4abc

(c) 8abc

(d) 16abc

## Answer

Answer: d**Q.5. **n arithmetic means are inserted between 3 and 17. If the ratio of the last and the first arithmetic mean is 3 : 1, then n is equal to

(a) 5

(b) 6

(c) 7

(d) 9

## Answer

Answer: b**Q.6. **If the sum of 2n terms of the A.P. 2, 5, 8, 11,… is equal to the sum of n terms of A.P. 57, 59, 61, 63, …, then n is equal to

(a) 10

(b) 11

(c) 12

(d) 13

## Answer

Answer: b**Q.7. **An A.P. has a property that the sum of first ten terms is half the sum of next ten terms. If the second term is 13, then the common difference is

(a) 3

(b) 2

(c) 5

(d) 4

## Answer

Answer: b**Q.8. **Let a_{1}, a_{2}, a_{3}, a_{4} be in A.P. If a_{1} + a_{4} = 10 and a_{2}a_{3} = 24, then the least term of them is

(a) 1

(b) 2

(c) 3

(d) 4

## Answer

Answer: b**Q.9. **The sum of n terms of an A.P. is 2n + 3n^{2}. Which term of this A.P. is equal to 299?

(a) 11th

(b) 50th

(c) 35th

(d) 29th

## Answer

Answer: b**Q.10. **If the sum of the first ten terms of an A.P. is 4 times the sum of the first five terms, then the ratio of the first term to the common difference is:

(a) 1 : 2

(b) 2 : 1

(c) 1 : 4

(d) 4 : 1