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19. Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2,1/2

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$Required \, \, sum=2\times 128+4\times 32+8\times 8+16\times 2+32\times \frac{1}{2}$

$Required \, \, sum=64\left [ 4+2+1+\frac{1}{2}+\frac{1}{2^2} \right ]$

Here, $4,2,1,\frac{1}{2},\frac{1}{2^2}$ is a GP.

first term =a=4

common ratio =r

$r=\frac{1}{2}$

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

$S_5=\frac{4(1-\left ( \frac{1}{2} \right )^5)}{1-\frac{1}{2}}$

$S_5=\frac{4(1-\left ( \frac{1}{2} \right )^5)}{\frac{1}{2}}$

$S_5=8(1-\left ( \frac{1}{32} \right ))$

$S_5=8(\frac{31}{32})$

$S_5=\frac{31}{4}$

$Required \, \, sum=64\left [ \frac{31}{4} \right ]$

$Required \, \, sum=16\times 31=496$

Posted by

seema garhwal

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