Question

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

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

Answer 1

The correct option is C $-13.5$

Given,

$x,2x+2,3x+3$ are in GP

$\Rightarrow \frac{2x+2}{x}=\frac{3x+3}{2x+2}$

$(2x+2{)}^2=x(3x+3)$

$4x^2+4+8x=3x^2+3x$

$x^2+5x+4=0$

$(x+4)(x+1)=0$

$\therefore x=-1,-4$

when $x=-1$ the numbers are

$-1,0,0$ then fourth term is $0$

when $x=-4$ the numbers are

$-4,-6,-9$

common ratio is $\frac{3}{2}$

then fourth term is $a{r}^3=-4\times \frac{3^3}{2^3}=-\frac{27}{2}=-13.5$