Question

Which term of the GP.
(i) 2, 8, 32, ..... is 512 ? (ii) 3, 3, 3 3 ...... is 729 ?
(iii)1/3, 1/9, 1/27, ..... is 1/2187?

Answer 1

The Geometric Progression is given as

$a,ar,ar^{2},ar^{3} ,ar^{4},............,ar^{n-1},ar^{n}$

The term can said to be

$a_{1},a_{2}, a_{3}, a_{4},......., a_{n-1},a_{n}$

Where,$a_{n} = ar^{n-1}$

and sum is given as $a\frac{r^{n-1}-1 }{r-1}$

(i) 2, 8, 32, ..... is 512

a=2  and r = 4

Hence in GP

(ii) 3, 3, 3 3 ...... is 729

a=3 ,r=1 Hence in GP

(iii)1/3, 1/9, 1/27, ..... is 1/2187

a= 1/3, r=1/3

Hence in GP.

Hope it helps

Thanks

With Regards

Answer 2

hence the answer is the fifth term
there is another formula too to solve this
I preferred this way
hope it helps