Question

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

Answer 1

The correct option is D

-13.5

Given that x, 2x + 2, 3x + 3 are in G.P.

Therefore, $(2x+2{)}^2$ = $x(3x+3)\Rightarrow x^2+5x+4$ =0

$\Rightarrow (x+4)(x+1)$ = 0 $\Rightarrow x$ = -1, -4

First term a = -4 (substituting x as -1 will make all terms zero)

Second term ar = $2(x+1)\Rightarrow -6$

Common ratio r = $\frac{-6}{-4}$ = $\frac{3}{2}$

then $4^{th}$ term = $a{r}^3$ = -4 x $\frac{3}{2}$ x $\frac{3}{2}$ x $\frac{3}{2}$

= $-\frac{27}{2}$ = -13.5