Question

If $x,2x+2$ and $3x+3$ are in G.P. then the next term in this sequence is

• A. $27$
• B. $-27$
• C. $\frac{27}{2}$
• D. $-\frac{27}{2}$

Answer 1

Answer: (D)

$-\frac{27}{2}$

Let $x=a,2x+2=b,3x+3=c$

$b^2=ac$

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

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

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

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

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

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

$x=-1,-4$

When $x=-1$, GP is $-1,2(-1)+2,3(-1)+3$

$=-1,0,0$

When $x=-4$

GP is$-4,2(-4)+2,3(-4)+3$

$=-4,-6,-9$

$a=-4,r=\frac{3}{2}$.

Fouth term is $a{r}^3=-4\times \frac{27}{8}=\frac{-27}{2}$