Question

The nth term of as a G.P is 2(1/2) ^(n-1) .if the sum of terms is 127/32. find the number of terms

Answer 1

nth term of as a G.P is 2(1/2) ^(n-1)
we know term(n) = a r^(n-1)

by comparison, we can see that a = 2, r = 1/2

If by "if the sum of terms is 127/32" you mean
the sum of the n terms, then

sum(n) = a(1 - r^n)/(1-r) , if | < 1
= 2( (1 - 1/2)^(n-1) ) )/(1 - 1/2)
= 4(1 - (1/2)^(n-1) )
= 2^2 (1 - 2^(1-n) )
= 4 - 2^(3-n)

Answer 2

Pressed "submit" too soon

so ....
127/32 = 4 - 2^(3-n)
2^(3-n) = 4 - 127/32 = 1/32 = 2^-5

3-n = -5
-n = -8
n = 8