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

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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