Discussion Forum



1)

If the 2nd, 5 th and 9th  terms  of a non-constant AP are in GP., then the common ratio of this GP is 


A) $\frac{8}{5}$

B) $\frac{4}{3}$

C) 1

D) $\frac{7}{4}$

Answer:

Option B

Explanation:

Let a be the first term and d be the common difference. Then , we have a+d, a+4d, a+8d in GP

 i.e., (a+4d)2 = (a+d)(a+8d)

$\Rightarrow a^{2}+16d^{2}+8ad= a^{2}+8ad+ad+8d^{2}$

$\Rightarrow 8d^{2}=a d       $

$\Rightarrow 8d=a $     [ d≠ 0]

Now, 

   common ratio

 $r=\frac{a+4d}{a+d}$

      $=\frac{8d+4d}{8d+d}$

              $=\frac{12d}{9d}$=$\frac{4}{3}$