Question

An infinite geometric progression a1 , a2 , a3 ,... has the property that an = 3(an+ l + an+2 +….) for every n ≥ 1. If the sum a1 + a2 + a3 +….... = 32, then a5 is

• A. 1/32
• B. 2/32
• C. 3/32
• D. 4/32

Answer 1

The Correct Option is C

The correct answer is (C):
For any n ≥ 1, an = 3 (an+1 + an+2 + ……..)
∴ a1 = 3 (a2 + a3 + ……) or r = 1/4 and
a1+a2+a3+... = 4a1/3 = 32 (given) ∴ a1 = 24
The G.P. is 24, 6, 1.5, 1.5/4, 1.5/16....
∴ a5 = 1.5/16 = 3/32