Question

The next term of G.P. $x,x^2+2,x^3+10$ is

• A. $0$
• B. $6$
• C. $\frac{729}{16}$
• D. $54$

Answer 1

Answer: (C), (D)

The correct options are
C $\frac{729}{16}$
D $54$

$\sin cex,x^2+2,x^3+10areinG.P$

$\therefore {(x^2+2)}^2=x(x^3+10)$

$\Rightarrow x^4+4x^2+4=x^4+10x$

$\Rightarrow 4x^2-10x+4=0$

$\Rightarrow 2x^2-5x+2=0$

$\Rightarrow x=2,\frac{1}{2}$

$Whenx=2$

$G.P2,6,18$

$r=\frac{6}{2}=3$

$nexttermofG.P=18\ast 3=54$

$Whenx=\frac{1}{2}$

$G.P\frac{1}{2},\frac{9}{4},\frac{81}{8}$

$r=\frac{\frac{9}{4}}{\frac{1}{2}}=\frac{9}{2}$

$nexttermofG.P=\frac{81}{8}\ast \frac{9}{2}=\frac{729}{16}$