Question

The fourth term of the G.P. x, 2x+2, 3x+3,... is
(a) -27/2 (b) -29/2 (c) -15/2 (d) -11/2

Answer 1

x, 2x+2, 3x+3 are in GP
(2x+2)^2 = x(3x+3). GM condition
4x^2 + 8x + 4 = 3x^2 + 3x
x^2 + 5x + 4 = 0
x^2 + 4x + x + 4 = 0
x(x + 4) + 1(x + 4) = 0
(x+4)(x+1) = 0
x = -1. or. x = -4

If x= -1
the GP is -1, 2(-1)+2, 3(-1) +3
-1, 0, 0
therefore t4 is 0
If x= -4
the GP is -4, 2(-4)+2, 3(-4)+3
-4, -6, -9
common ratio = 3/2
a = -4
t4 = -4(3/2)^3
= -4(27/8)
= -27/2
forth term is -27/2

Answer 2

Your ans . is here ...hope it will help u..