Question

The first term of a G.P. is $1.$ If the sum of the third and the fifth term is $90,$ then the common ratio is

• A. $-\sqrt{10}$
• B. $\sqrt{10}$
• C. $-3$
• D. $3$

Answer 1

Answer: (C), (D)

The correct options are
C $-3$
D $3$

The given G.P. is $1,r,r^2,\dots$
Now, $r^2+r^4=90$
$\Rightarrow r^4+r^2-90=0\Rightarrow (r^2+10)(r^2-9)=0\Rightarrow r=\pm 3$