NCERT Class XI Mathematics - Sequences and Series - Solutions

Question : 86

Total: 106

The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

Solution:

We have, a = 5, r = 2
Let the number of terms be n whose sum is 315.
Then

a(4n−1)

r−1

= 315 ⇒

5(2n−1)

2−1

= 315
⇒ 2n−1 = 63 ⇒ 2n = 64 ⇒ 2n = (2)6
∴ n = 6
Hence, the last term = arn−1 i.e., a6 = 5(2)6−1 = 5(2)5 = 160

Go to Question:

Prev Question

Next Question