Question

Let $\{T_n\}$ be a sequence of integers in G.P. in which $T_4:T_6=1:4$ and $T_2+T_5=216$ . then $T_1$ is

• A. 14
• B. 12
• C. 16
• D. none of these.

Answer 1

Answer: (B)

$\frac{T_4}{T_6}=\frac{a{R}^3}{a{R}^5}=\frac{1}{4}$
$\Rightarrow R^2=4$
$\Rightarrow R=2$
$T_2+T_5=216$
$\Rightarrow aR+a{R}^4=216$
$\Rightarrow aR\left(1+R^3\right)=216$
$\Rightarrow a\cdot 2\left(1+8\right)=216$
$\Rightarrow a\left(1\right)=\frac{108}{9}=12$.
$Thus{T}_1=a=12.$