Question

the nth term of a gp is 128 and the sum of its nth term is 255 If its common ratio is 2 then find its first term

Answer 1

It is given that nth term( or last term ) of the GP is 128 and the sum of n terms of the same GP is 255, with the common ratio of 2.


Let the first term of the GP be a,

So,
nth term or last term = 128

sum of n terms = 255


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From the properties of geometric progression, we know

$S_{n} = \dfrac{lr - a}{r - 1} \text{ , where r} ≠ \text{ 0 and l is the last term of the GP}$


Thus,

$\implies 255 = \dfrac{(128 \times 2 ) - a}{2-1}\\\\\\\implies 255= \dfrac{256-a}{1}\\\\\\\implies a= 256-255$

a = 1


Hence, first term of the geometric progression is 1.

Answer 2

Answer:

1

Step-by-step explanation:

nth term of a GP is 128.

t(n) = 128

a.rⁿ⁻¹ = 128

a. (rⁿ/r) = 128

a.rⁿ = 128 * r

Common ratio is 2.

a.rⁿ = 128 * 2

a.rⁿ = 256     ------- (i)

Also, nth term is 255.

[a(rⁿ - 1)/r - 1] = 255

[(a.rⁿ - a)/2 - 1] = 255

[256 - a/2 - 1] = 255

[256 - a/1] = 255

[256 - a] = 255

a = 1.

The first term a = 1.

Hope it helps you

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