If 5^(th) term of a G.P is 32 and common ratio 2, then the sum of 14 terms is

Correct option is (A) 32,766

Let first term of G.P. be a.

Given that common ratio is r = 2.

\(\therefore5^{th}\) term of G.P. is \(a_5=ar^4\)       \((\because a_n=ar^{n-1})\)

\(\Rightarrow ar^4=32\)

\(\Rightarrow a.2^4=32\)

\(\Rightarrow a=\frac{32}{2^4}=\frac{32}{16}=2\)

Sum of first 14 terms is \(S_{14}=\frac{a(r^{14}-1)}{r-1}\)    \(\left(\because S_{n}=\frac{a(r^{n}-1)}{r-1}\right)\)

\(=\frac{2(2^{14}-1)}{2-1}\)                 \((\because a=2\;\&\;r=2)\)

= 2 (16384 - 1)           \((\because2^{14}=16384)\)

= 32766

Correct option is A) 32, 766