Question

The sum of all the positive terms in the geometric sequence 54, - 36, 24, - 16, ... is

A. 32.4

B. 97.2

C. 121.5

D. 162. 1​

Answer 1

B. 97.2

Explanation:

The sequence of positive terms is ...

54, 24, 10 2/3, 4 20/27, ...

This sequence has first term 54 and common ratio 24/54 = 4/9. The sum of the infinite series is ...

S = a1/(1 -r) = 54/(1 -4/9) = 54(9/5)

S = 97.2

The sum of the positive terms in the infinite series is 97.2.