Question

Match each of the following GPs with the correct next terms.

• A. 32
• B. 8
• C. 81
• D. $x^{4}y$

Answer 1

In the GP $2,2\sqrt{2},4,4\sqrt{2},$
$a=2,r=\frac{2\sqrt{2}}{2}=\sqrt{2}.$
The $t^{\text{th}}$ term of a GP of first term $a$ and common ratio $r$ is given by
$t_n=a{r}^{n-1}.$
$\Rightarrow t_5=2(\sqrt{2}{)}^4=8$

In the GP $xy,x^{2}y,x^{3}y,$
$a=xy,r=\frac{x^{2}y}{xy}=x.$
$\Rightarrow t_4=xy\times x^3=x^{4}y$

In the GP $4,8,16,$
$a=4,r=\frac{8}{4}=2.$
$\Rightarrow t_4=4\times 2^3=32$

In the GP $3,9,27,$
$a=3,r=\frac{9}{3}=3.$
$\Rightarrow t_4=3\times 3^3=81$