Question

Find $4th$ and $8th$ terms of the G.P. $0.008,0.04,0.2,.........$

Answer 1

It is given that the first term of G.P is $a_1=0.008$ and the second term is $a_2=0.04$, therefore,

$r=\frac{a_2}{a_1}=\frac{0.04}{0.008}=5$

We know that the formula for the $n$th term of an G.P is $T_n=a{r}^{n-1}$, where $a$ is the first term, $r$ is the common ratio.

It is given that the first term is $a=0.008$ and the common ratio is $r=5$, thus,

$T_4=0.008\times {\left(5\right)}^{4-1}=0.008\times 5^3=0.008\times 125=1$

$T_8=0.008\times {\left(5\right)}^{8-1}=0.008\times 5^7=0.008\times 78125=625$

Hence, $T_4=1$ and $T_8=625$.