Question

Write three terms of the $GP$ when the first term $a$ and the common ratio $r$ are given

A)$a=4:r=3$

B)$a=\sqrt{5};r=\frac{1}{5}$

C)$a=81;r=\frac{-1}{3}$

D)$a=\frac{1}{64};r=2$

Answer 1

As we know that, in a G.P.-

$a_n=a{r}^{n-1}$

Therefore,

• (A) $a=4;r=3$

First term $=4$

$a_2=ar=4\times 3=12$

$a_3=a{r}^2=4\times 3^2=36$

• (B) $a=\sqrt{5};r=\frac{1}{5}$

First term $=\sqrt{5}$

$a_2=ar=\sqrt{5}\times \frac{1}{5}=\frac{\sqrt{5}}{5}=\frac{1}{\sqrt{5}}$

$a_3=a{r}^2=\sqrt{5}\times {\left(\frac{1}{5}\right)}^2=\frac{\sqrt{5}}{25}=\frac{1}{5\sqrt{5}}$

• (C) $a=81;r=\frac{-1}{3}$

First term $=81$

$a_2=ar=81\times \frac{-1}{3}=-27$

$a_3=a{r}^2=81\times {\left(\frac{-1}{3}\right)}^2=9$

• (D) $a=\frac{1}{64};r=2$

First term $=\frac{1}{64}$

$a_2=ar=\frac{1}{64}\times 2=\frac{1}{32}$

$a_3=a{r}^2=\frac{1}{64}\times 2^2=\frac{1}{16}$