Question

Check whether-256is term of GP:-4,-5,-16

Answer 1

First of all, the correct question is :

Check whether -256 is a term of Gp -4,-8,-16

Given:

(i) The terms of GP are -4, -8, -16...

To find:

(i) -256 belongs to the GP or not.

Solution:

Let us first find the common multiple between two consecutive terms (r).

r = (-8/-4)

= 2

nth term in the GP is given as:

an = $ar^{n-1}$

Here, a is the first term = -4

r = 2

So, an = $(-4)*2^{n-1}$

Let the nth term be -256.

So, $(-4)*2^{n-1}$ = 256

$2^{n-1} = 256/-4\\ = -64\\= -2^{6}$

Ignoring the term, we get,

n - 1 = 6

⇒ n = 7

So, -256 is the 7th term of the GP.