Question

The twentieth term of the GP $\frac{5}{2},\frac{5}{4},\frac{5}{8}$, ... is

• A. $\frac{5}{2^{19}}$
• B. $\frac{5}{2^{20}}$
• C. $\frac{5}{2^{10}}$
• D. $\frac{5}{{10}^{11}}$

Answer 1

The correct option is B $\frac{5}{2^{20}}$

In given GP, we have $a=\frac{5}{2},r=\frac{1}{2}$

We know that nth term of a GP is given by $a{r}^{n-1}$

$\therefore t_{20}={\frac{5}{2}\left(\frac{1}{2}\right)}^{19}=\frac{5}{2^{20}}$