Question

The nth term of a g.p is 128 and sum of its n term is 255.if its common ratio is 2 ,then finds its first term.

Answer 1

Answer:

First term of the g.p.  = 1

Step-by-step explanation:

Let the firt term of the geometric progression = x

Common ration = 2

∴ 2nd term of the g.p. = 2x

∴ 3rd term  = (2²)x

....

N th term can be written as = ($2^{n}$)x

Sum of the n terms S = 255

as we can see, except x, all other terms in the g.p. are multiples of 2

and sum of all the terms is an odd number.

∴ x must be an odd number.

now nth term

($2^{n}$)x  = 128 =  ($2^{7}$) × 1

There are no factors of odd numbers in 128, except 1

∴ x = 1

Series of g.p. is

1, 2, 4, 8, 16, 32, 64, 128

Checking the sum of the n terms,

1+2+4+8+16+32+64+128 = 255

∴ First term of the g.p. = 1

Answer 2

Answer:

1

Step-by-step explanation:

The nth term of a g.p is 128 and sum of its n term is 255.if its common ratio is 2 ,then finds its first term.

Let say GP is

a  , ar , ar²

r = 2

so GP

a  , 2a , 4a  ,      

nth term = a2^(n-1) = 128

Sum of n terms of GP

a(1 - r^n)/(1-r)  

= a( 1 - 2^n)/(1-2)

= a(2^n  - 1)

a(2^n  - 1)  = 255

a2^(n-1) = 128

(2^n  - 1) /2^(n-1) = 255/128

=> 2 - 1/2^(n-1)  = 255/128

=> 1/2^(n-1) = 1/128

=> 2^(n-1) = 128

=> n-1 = 7

=> n = 8

a2^(n-1) = 128

=> a 2^7 = 128

=> a * 128 = 128

=> a = 1