Question

Find the fifth term of the G.P. $\frac{3}{2},\frac{3}{4},\frac{3}{8},..........$

Answer 1

We can see that: $a=\frac{3}{2},r=\frac{T_2}{T_1}=\frac{\frac{3}{4}}{\frac{3}{2}}=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2},T_5=?$
$T_n=a{r}^{n-1}$
$T_5=\frac{3}{2}{\left(\frac{1}{2}\right)}^{5-1}=\frac{3}{2}{\left(\frac{1}{2}\right)}^4=\frac{3}{2}\times \frac{1}{16}=\frac{3}{32}$