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

Answer: (D)

$x,2x+2,3x+3$ are in $G.P$.
$\Rightarrow (2x+2{)}^2=x(3x+3)$
$\Rightarrow 4x^2+8x+4=3x^2+3x$
$\Rightarrow x^2+5x+4=0$
$\Rightarrow x=-1,-4$
So, the GP is $-4,-6,-9,\dots$
(considering $x=-4,$ as for $x=-1$ $2x+2=0)$
Hence, fourth term is $-9\times 1.5=-13.5$