Question

4. The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is
then find its first term.​

Answer 1

ANSWER

From the question it is given that, 

The nth  term of a G.P. Tn=128 

The sum of its n terms Sn=255

Common ratio r=2 

We know that, Tn=arn−1

128=a2n−1a=128/2n−1

Also we know that, 

Sn=(r−1)a(rn−1)

255=a(2−1)(2n−1)

By cross multiplication we get,

255=a(2n−1)a=(2n−1)255

Now, consider both the equation(i) and equation (ii)

(2n−1)255=(2n−1)128

By cross multiplication we get, 

255×2n−1=128(2n−1)

255×2n−1=128×2