Question

Find the last term of the following sequence $2,4,8$........ to $9$ terms

Answer 1

It is given that the first term of G.P is $a_1=2$ and the second term is $a_2=4$, therefore,

$r=\frac{a_2}{a_1}=\frac{4}{2}=2$

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 $a=0.008$, number of terms are $n=9$ and the common ratio is $r=2$, thus,

$T_9=2\times {\left(2\right)}^{9-1}=2\times 2^8=2\times 256=512$

Hence, the last term is$512$.