Question

Lesson 1 Homework

Answer 1

128

This question requires us to solve an infinite GP

As we can see the first unit is 16 wide, then 8, then 4 and so on; this can be written as  

$64(1,0.5,0.25,0.125,....$$\infinity$∞$)$  (64 used as 16*4 = 64 is the area of the first rectangle)

We have  $S$∞$=a/(1-r)$ where a is the first term and r is the common ratio of the GP for summing an infinite GP.

here we have  

$a=64 \\ r=0.5$

Therefore

$S$∞$=\frac{64}{1-0.5} \\\\=\frac{64}{0.5} \\\\=128$

Learn more about GP here

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