Question

Find the last term of the following sequence $2,3,4\frac{1}{2}$ ........ to 6 terms

Answer 1

It is given that the first term of G.P is $a_1=2$ and the second term is $a_2=3$, therefore,

$r=\frac{a_2}{a_1}=\frac{3}{2}$

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 $a=2$, number of terms are $n=6$ and the common ratio is $r=\frac{3}{2}$, thus,

$T_6=2\times {\left(\frac{3}{2}\right)}^{6-1}=2\times {\left(\frac{3}{2}\right)}^5=2\times \frac{3^5}{2^5}=\frac{243}{16}$

Hence, the last term is$\frac{243}{16}$.