Find the 7th and nth terms of the GP


Find the $7^{\text {th }}$ and $n$th terms of the GP $0.4,0.8,1.6 \ldots$



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, $\mathrm{r}=\frac{\mathrm{a}_{2}}{\mathrm{a}_{1}}$


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,

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


$=(0.2) 2^{n}$

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

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now