Question

If $x,2x+2,3x+3,.....$ are in GP, then the fourth term is

• A. $27.5$
• B. $4x+5$
• C. $-13.5$
• D. $4x+4$

Answer 1

Answer: (C)

Since, given series is in GP.
$\therefore$ ${(2x+2)}^2=x\times (3x+3)$
$\Rightarrow$ $4x^2+4+8x=3x^2+3x$
$\Rightarrow$ $x^2+5x+4=0$
$\Rightarrow$ $x=\frac{-5\pm \sqrt{25-16}}{2}$
$\Rightarrow$ $x=\frac{-5\pm 3}{2}$
$\Rightarrow$ $x=-\frac{8}{2}=-4$ and $x=-\frac{2}{2}=-1$ At $x=-1,$
second terms become zero so we neglect that.
At $x=-4,a=-4,r=3/2$
$\therefore$ $T_4=-4\times {(3/2)}^3=-\frac{27}{2}=-13.5$