Question

If x,2x+2,3x+3 are successive terms of GP then what is the fourth term?​

Answer 1

Answer:

Then x(3x+3)=(2x+2)^2

Or 3x^2 +3x = (2x)^2 +4 +8x

Or x^2 +5x +4=0

Or (x+1)×(x+4)=0

So x=-1 or x=-4 = First term

Common ratio = T3/T2 =3×(x+1)÷2×(x+1)=3/2.

Shortcut to find T4 :

T4×T2 = T3^2

So T4×2(x+1) = 9×(x+1)^2

So T4 = 9×(x+1)/2 Answer without finding a & r.

MORAL or LESSONS LEARNT

Get Answer in direct or shortest way possible, if Required in nonconventional or nontraditional methods.

Hope this helps you all in future.