Question

sum of 4 terms of g p is 30 & sum of first and last term is 18 . Find gp

a(r^4-1)/(r-1) = 30
a + ar^3 = 18

a(1+r^3) = 18
it's easy to see that if a=2, r=2
Does that work on S4?
2*15/1 = 30. Yes

So, the GP is

2,4,8,16,...

But sir I want not logic proof , please give complete proof

Answer 1

Geez, guy, you're not gonna work on it at all?

a = 30(r-1)/(r^4-1)
a = 18/(1+r^3)

30(r-1)(1+r^3) = 18(r^4-1)
30(r^4-r^3+r-1) = 18(r^4-1)
2r^4-5r^3+5r-2 = 0

I'll let you factor that and find that r=2 is a root.

Answer 2

Sir I only know to solve quadratic equation.

Answer 3

well, I gave you a hint. Try some synthetic division. You know that any rational roots must be found among

±1, ±1/2, ±2