CBSE Class 11 Mathematics Sequences And Series Worksheet Set B

 SEQUENCES AND SERIES

1. Find the sum of the first 19 terms of an AP when a₄ + a₈ + a₁₂ + a₁₆ = 224.

2. In an AP of n terms, prove that the sum of the k^th term from the beginning and the kth term fromthe end is independent of k and equal to the sum of the first and last terms.

3. Split 69 into three parts such that they are in AP and the product of the two smaller parts is 483.

4. If sum of infinite terms of G.P. is 15 and sum of squares of infinite terms of G.P. is 45, then find GP.

5. Find the rth term if the p^th term of an AP is q and the q^th term is p.

6. If (5n + 4) : (9n + 6) is the ratio of the sums of the n^th terms of two APs, then find out the ratio of their 13^th terms.

7. There are four numbers of which the first three are in G.P. and the last three are in AP, with a common difference of 6. If the first number and the last number are equal, then find the
numbers.

8. If a, b, c are in A.P. then prove that b + c, c + a, a + b are also in A.P.

9. If a, b, c are in A.P then prove that a²(b + c), b²(c + a), c² (a + b) are also in A.P.

10. Sum of n terms of the series, 6 + 66 + 666 + ….

11. The sum of the first three terms of an increasing G.P. is 21 and the sum of their squares is 189, then find the sum of its first n terms.

12. The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately
positive and negative, then find the first term of the G.P.

13. If the 2^nd , 5^th and 9th terms of an A.P. are in G.P., then find the common ratio of this G.P.

14. Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then find the common ratio of this G.P.

15. Use GP to represent 0. 23 4 5 as a rational number in p/q form.

 

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