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Question
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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Solution
The product of the corresponding terms of the sequence 2, 4, 8, 16, 32 and 128, 32, 8, 2, `1/2` is 2 × 128, 4 × 32, 8 × 8, 16 × 2, 32 × `1/ 2` or 256, 128, 64, 32, 16
First term of the geometric progression, a = 256
r = `128/256 = 1/2, "n" = 5`
∴ Sum = `(256[1 - (1/2)^5])/(1 - 1/2)`
= `256 xx 2 (1 - 1/32)`
= `256 xx 2 xx 31/32`
= 16 × 31
= 496
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