For a sequence if $S_{n}=\frac{5^{n}-2^{n}}{2^{n}}$, then its fourth term is

Question

Aicharya · Accepted Answer

$s_{n}=\frac{5^{n}-2^{n}}{2^{n}} ; s_{n-1}=\frac{5^{n-1}-2^{n-1}}{2^{n-1}}$ $\begin{aligned} T_{n} &=s_{n}-s_{n-1} \ T_{n} &=\frac{5^{n}-2^{n} \cdot 5^{n-1}}{2^{n}} \ T_{4} &=\frac{5^{4}-2 \cdot 5^{3}}{2^{4}} \ &=\frac{625-250}{16} \ &=\frac{375}{16} \end{aligned}$

For a sequence if $S_{n}=\frac{5^{n}-2^{n}}{2^{n}}$, then its fourth term is

Solution