Question

How many terms of the GP : 3, 3/2, 3/4,... are needed to give the sum 3069/512?

• A. 8
• B. 10
• C. 12
• D. 15

Answer 1

Answer:

B. 10

$a=3, r = 1/2$

$S_n=\frac{a(1-r^n)}{1-r}$

$3069/512=\frac{3(1-(1/2)^n)}{1-1/2}$

$3069/512=6(1-(1/2)^n)$

$3069/3072=1-(1/2)^n)$

$(1/2)^n=1-(3069/3072)$

$1/2^n=3/3072$

$1/2^n=1/1024$

$2^n=1024=2^{10}$

$n=10$