Mark the correct alternative in each of the following: The nth term of a G.P. is 128 and the sum of its n terms is 225. If its common ratio is 2, then its first term is

Question

Philoid · Accepted Answer

Let say GP is

a,ar,ar²

where a is the first term and r is the common ratio

Also, given that r = 2

So, GP becomes

a,2a,4a

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

a.2^(n-1) = 128

⇒

⇒ a.2ⁿ = 256

Sum of n terms of GP

⇒

Substituting a²ⁿ in above equation we get

-255 = a-256

a =1.

Mark the correct alternative in each of the following:The nth term of a G.P. is 128 and the sum of its n terms is 225. If its common ratio is 2, then its first term is

Mark the correct alternative in each of the following:
The nth term of a G.P. is 128 and the sum of its n terms is 225. If its common ratio is 2, then its first term is