Find the 7th and nth terms of the GP

Solution:

Given GP is 0.4, 0.8, 1.6….

The given GP is of the form, $a, a r, a r^{2}, a r^{3} \ldots$

Where $r$ is the common ratio.

First term in the given GP, $a_{1}=a=0.4$

Second term in GP, $a_{2}=0.8$

Now, the common ratio, $\mathrm{r}=\frac{\mathrm{a}_{2}}{\mathrm{a}_{1}}$

$r=\frac{0.8}{0.4}=2$

Now, $\mathrm{n}^{\text {th }}$ term of GP is, $\mathrm{a}_{\mathrm{n}}=\mathrm{ar}^{\mathrm{n}-1}$

So, the $7^{\text {th }}$ term in the GP,

$a_{7}=a r^{6}$

$=0.4 \times 2^{6}$

= 25.6

$\mathrm{n}^{\text {th }}$ term in the GP,

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

$=(0.4)(2)^{n-1}$

$=(0.2) 2^{n}$

Hence, $7^{\text {th }}$ term $=25.6$ and $\mathrm{n}^{\text {th }}$ term $=(0.2) 2^{\mathrm{n}}$