Question

The n^th 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 

A. 1 

B. 3 

C. 8 

D. none of these

Answer 1

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Answer 2

Correct answer is A. 1

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 n^th term = ar (n-1) = 128 

a. 2^(n-1) = 128

⇒ a.2ⁿ = 256 

Sum of n terms of GP

Substituting a ²ⁿ in above equation we get 

-255 = a-256 

a =1.