Question

Given the geometric progression $3,6,12,24,....$ The term $12288$ would occur as the

• A. ${11}^{th}term$
• B. ${12}^{th}term$
• C. ${13}^{th}term$
• D. ${14}^{th}term$

Answer 1

The correct option is C ${13}^{th}term$

From given GP, we have

$a=3,r=2,a_n=12288$

$\therefore 12288=3\times 2^{(n-1)}$

$\Rightarrow 4096=2^{(n-1)}$

$\Rightarrow 2^{12}=2^{(n-1)}$

$\Rightarrow 12=n-1$

$\Rightarrow n=13$