Question

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

Answer 1

The product of the corresponding terms of the sequence 2, 4, 8, 16, 32 and 128, 32, 8, 2, ${\displaystyle \frac{1}{2}}$ is 2 × 128, 4 × 32, 8 × 8, 16 × 2, 32 × ${\displaystyle \frac{1}{2}}$ or 256, 128, 64, 32, 16

First term of the geometric progression, a = 256

r = ${\displaystyle \frac{128}{256}=\frac{1}{2},\text{n}=5}$

∴ Sum = ${\displaystyle \frac{256[1-{\left(\frac{1}{2}\right)}^5]}{1-\frac{1}{2}}}$

= ${\displaystyle 256\times 2(1-\frac{1}{32})}$

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

= 16 × 31

= 496