Question

The fourth term of G.P. $x^3+10,x^2+2,x$ can be

• A. $1$
• B. $6$
• C. $\frac{2}{3}$
• D. $\frac{1}{9}$

Answer 1

Answer: (C), (D)

The correct options are
C $\frac{2}{3}$
D $\frac{1}{9}$

We have,
$x(x^3+10)=(x^2+2{)}^2$ (Terms of a G.P.)
$\Rightarrow 4x^2-10x+4=0$
$\Rightarrow x=2or\frac{1}{2}$
$\Rightarrow r=\left[\frac{x}{x^2+2}\right]$
Therefore, next term $\left[\frac{x^2}{x^2+2}\right]=\frac{4}{4+2}=\frac{2}{3}$
or $\frac{\left(1/4\right)}{\left(1/4\right)+2}=\frac{1}{1+8}=\frac{1}{9}$