Question

Find the ${20}^{th}and{n}^{th}$ terms of the G.P.

$\frac{5}{2},\frac{5}{4},\frac{5}{8}...$

Answer 1

Here $a=\frac{5}{2}andr=\frac{\frac{5}{4}}{\frac{5}{2}}=\frac{1}{2}$

We know that $a_n=a{r}^{n-1}$

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

$a_n=\frac{5}{2}\times {\left(\frac{1}{2}\right)}^{n-1}=\frac{5}{2\times 2^{n-1}}=\frac{5}{2^n}$