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

Solution:

The given sequences are

2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2.

Accordingly, the required sum,

S = 2 x 128 + 4 x 32 + 8 x 8 + 16 x 2 + 32 x 1/2²

64 [4 + 2 + 1 + 1/2 + 1/2² ....(1)

It can be seen 4, 2, (1 + 1/2), 1/2² is a G.P.

Here, a = 4 and r = 1/2

It is known that S_n = a (1 - rⁿ)/(1 - r)

Therefore,

S₅ = a (4 - (1/2)ⁿ)/(1 - 1/2)

= 4 [1 - 1/32]/(1/2)

= 31/4

Hence,

[4 + 2 + 1 + 1/2 + 1/2²] = 31/4

Putting this value in (1) , we obtain

S = 64 x 31/4

= 16 x 31

= 496

Thus, the required sum is 496

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 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

Summary:

The sum of the products of the corresponding terms of the sequences 2, 4, 8, 16 and 128, 32, 8, 2.. is 496. Therefore the required sum is 496