Question

Find the $8^{\mathrm{th}}$ term of the GP : $0.3,0.06,0.012,\dots$

Answer 1

Find the $8^{\mathrm{th}}$ term of the GP :

Here, the sequence is $0.3,0.06,0.012,\dots$

First term $a=0.3$

Common difference $r=\frac{0.06}{0.3}=0.2$

The general term of GP is $a_n=a{r}^{n-1}$

$\begin{array}{rcl}& \Rightarrow & a_8=a{r}^{n-1}\\ & =& (0.3)\times {\left(0.2\right)}^{8-1}\\ & =& 0.3\times {\left(0.2\right)}^7\end{array}$

Hence, $8^{\mathrm{th}}$ term of given GP is $\begin{array}{rcl}& & 0.3\times {\left(0.2\right)}^7\end{array}$.