Question

The sum of the products of the corresponding terms of the sequences $2,4,8,16,32$ and $128,32,8$, $2,\frac{1}{2}$ is

• A. 496
• B. 390
• C. 450
• D. 466

Answer 1

Answer: (A)

Given, sequences are $2,4,8,16,\mathrm{32....}$(i)
and $128,32,8,2,\frac{1}{2}....$(ii)
Multiplying the corresponding terms of (i) and (ii) to obtain a new sequence $256,128,64,32,16$.
Let $S=256+128+64+32+16$
Here, $a=256,r=\frac{1}{2}$
$\therefore$ Required sum $S=\frac{256\left[1-{\left(\frac{1}{2}\right)}^5\right]}{1-\frac{1}{2}}$
$[\because S_n=\frac{a\left(1-r^n\right)}{1-r}$ as $r\propto 1]$
$=256\times 2\left(1-\frac{1}{2^5}\right)$
$=512\times \left(1-\frac{1}{32}\right)$
$=512\left(\frac{32-1}{32}\right)$
$=16\times 31$
$=496$