Question

The first and eight terms of a G.P. are $x^{-4}$ and $x^{52}$ respectively. If the second term is $x^t$, then t is equal to:

• A. -13
• B. 4
• C. $\frac{5}{2}$
• D. 3

Answer 1

Answer: (B)

Let a be the first term and r be the common ratio so, general term of G.P is $T_n=a{r}^{n-1}$
As given,
$T_1=x^{-4}=aand{T}_8=a{r}^7=x^{52}\therefore a{r}^7=x^{52}$
$\Rightarrow x^{-4}{r}^7=x^{52}\Rightarrow r^7=x^{56}$
$\Rightarrow r^7={\left(x^8\right)}^7\Rightarrow r=x^8$
$\therefore T_2=a{r}^1=x^{-4}.x^8$
$T_2=x^4$
But $T_2=x^t\Rightarrow x^t=x^4\Rightarrow t=4$