Question

The first term of GP exceed the second term by 2 and the sum to infinity is 15 find the series and the sum of first 5 term

Answer 1

first term --- a
second term ---- ar

a - ar = 2
a(1-r) = 2

sum to infinity = 15
a/(1-r) = 15

[a(1-r)][a/(1-r)] = 2(15)
a^2 = 30
a = ± √30

from a = ar+2
√30 = √30r + 2
r = (√30 - 2)/√30 = 1 - 2/√30

so we have √30, √30 + 2 , ....

sum(5) = a (r^5 - 1)/(r-1)
= ....
= .....

I will leave the cleanup up to you