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

1.	If 5th term of a G.P is 32 and common ratio 2, then the sum of 14 terms is A) 64,432 B) 16,383C) 32,766 D) 8,194
Answer» Correct option is (C) 32,766 Let a & r be the first term & common difference of G.P. \(\therefore\) r = common difference = 2 and \(a^5=32\) \(\Rightarrow ar^4=32\) \(\Rightarrow a=\frac{32}{r^4}=\frac{32}{2^4}\) \(=\frac{32}{16}=2\) \(\therefore\) Sum of 14 terms is \(S_{14}=\frac{a(r^{14}-1)}{r-1}\) \(=\frac{2(2^{14}-1)}{2-1}\) \(=2(16384-1)\) \(=2\times16383=32766\) Hence, sum of 14 terms in G.P. is 32766. Correct option is C) 32,766

If 5th term of a G.P is 32 and common ratio 2, then the sum of 14 terms is A) 64,432 B) 16,383C) 32,766 D) 8,194

Answer»

Correct option is (C) 32,766

Let a & r be the first term & common difference of G.P.

\(\therefore\) r = common difference = 2

and \(a^5=32\)

\(\Rightarrow ar^4=32\)

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

\(=\frac{32}{16}=2\)

\(\therefore\) Sum of 14 terms is \(S_{14}=\frac{a(r^{14}-1)}{r-1}\)

\(=\frac{2(2^{14}-1)}{2-1}\)

\(=2(16384-1)\)

\(=2\times16383=32766\)

Hence, sum of 14 terms in G.P. is 32766.

Correct option is C) 32,766