Question

The third term of the sequence whose $n^{th}$ term is $\frac{1}{n^2}+1$ is k.Find 9k

Answer 1

Given that:-

$T_n=\frac{1}{n^2}+1$

To find:- $T_3=?$

Solution:-

For $n=3$, we get the $3^{rd}$ term.

$\therefore T_3=\frac{1}{3^2}+1$

$\Rightarrow T_3=\frac{1}{9}+1$

$\Rightarrow T_3=\frac{1+9}{9}=\frac{10}{9}$.

Hence the correct answer is $\frac{10}{9}$

$k=\frac{10}{9}$

$9k=10$