Geometric Sequence and Series

Question

Suppose that after a tax rebate an individual spends $210. The money is then respent over and over again, each time at a rate of 70%. Determine the total amount spent. Assume that the money can be respent an infinite number of times.

Answer 1

The way I am reading this it appears he spends

$210, then 70% of 210 or $147, then 70% of 147 or $102.90,

and so on.

 

So you have a common ratio of r = 0.7

 

a₁ =210
r = .7
 
For an infinite geometric series there is a sum so long as |r|<1
Since r = 0.7<1 This has a sum:

 

∞

∑ 210(.7)^n-1

n=1

 

 

S = a₁/(1-r) = 210/(1-.7) = 210/.3 = $700