Question

Let $\left(a_1, b_1\right)$ and $\left(a_2, b_2\right)$ are the pair of real numbers such that $10, a, b, a b$ constitute an A.P. Then the value of $\left(\frac{2 a_1 a_2+b_1 b_2}{10}\right)$ is equal to

• A. 1
• B. 2
• C. 3
• D. 5

Answer 1

Answer: (C)

Let $ a =10+ d , b =10+2 d , ab =10+3 d $
$\Rightarrow (10+d)(10+2 d)=10+3 d \Rightarrow 2 d^2+27 d+90=0$
$\Rightarrow d =-6 \text { or } d =\frac{-15}{2} $