If the 1st,2nd,3rd term of a G.P areX,X+1,X+4 respectively,find X

Answer 1

a = X
a r = X+1
so
r = (X+1)/X
a r^2 = X+4
so
X [(X+1)/X ]^2 = X + 4

(1/X)(X^2 + 2 X + 1) = X + 4

X^2 + 2 X + 1 = X^2 + 4 X

X = 1/2