Question

Find the sum of the product of the corresponding terms of the sequences 2, 4 ,16 and 32 128, 32, 8 ,2 $\frac{1}{2}$.

Answer 1

When we multiply the corresponding terms of the sequences 2 4, 8, 16, 32, and 128.

32, 8, 2, $\frac{1}{2}$, We have :

$(2\times 128),(4\times 32),(8\times 8),(16\times 2),(32\times \frac{1}{2})$

i.e. 255, 128, 64, 32,16, which are in G.P.

Here a = 256, r = $\frac{128}{256}=\frac{1}{2}andn=5$

We know that

$S_n=\frac{a(1-r^n)}{1-r}$

$\therefore S_5=\frac{256[1-{\left(\frac{1}{2}\right)}^5]}{(1-\frac{1}{2})}$

= $256\times 2[1-\frac{1}{32}]$

= $256\times 2\times \frac{31}{32}=496$