Question

In a 64 terms GP if sum of total terms is seven times sum of odd terms, then common ratio is

(1) 3 

(2) 4 

(3) 5 

(4) 6

Answer 1

The correct option is (4) 6

a, ar, ar²,……ar⁶³ 

a + ar + ar²+…..+ar⁶³ = 7 [a + ar² + ar⁴+ …..+ar⁶²]

\(\frac{a(1-r^{64})}{(1-r)} = 7 \frac{a(1-r^{64})}{(1-r^2)}\)

1 + r = 7 

r = 6