If `x, 2x+ 2, 3x + 3 `are in `G.P. ,` then the fourth term is (A) `27` (B) `-27` (C)`13.5` (D)`-13.5`

Options

A. `27`
B. `-27`
C. `13.5`
D. `-13.5`

Answer

D

Explanation

If `x, 2x+2,3x+3` are ………….
Given that `x, 2x+2, 3x+3` are in G.P.
Therefore, `(2x+2)^(2)= x(3x+3)`
`implies x^(2)+5x+4 = 0`
`implies (x+4)(x+1) = 0`
`implies x = -1 -4`
Now first term `a = x`, second trem `ar = 2(x+1)`
`implies r= (2(x+1))/(x)`, then `4^(th)` term `= ar^(3)`
`= x[(2(x+1))/(x)]^(-3) = (8)/(x^(2))(x+1)^(3)`
Putting `x = -4`, We get
`T_(4)= (8)/(16)(-3)^(3) = -(27)/(2)= - 13.5`