What's your total income for working 31 days?

Question

Suppose you go to a company that pays $0.04 for the first day, $0.08 for the second day, $0.16 for the third day and so on. If the daily wage keeps doubling, what will your total income be for working 31 days?

Answer 1

it's a geometric sequence

a1 = .04

a2 = .08

a3 = .16

an = a1r^(n-1), r=2 = the common ratio

a31 = .04(2)^30

a31 = 42,949,672.96

double it, then subtract 4 cents to get s31

2a31 = 4 cents more than s31

2a31 = s31+a1

geometric sum formula for finite sequence is

sn = a1(1-r^n)/(1-r)

s31 = .04(1-2^31)/(1-2)= -.04(1-2^31) = -.04(-2147483647)= $85,899,345.88

= about 86 million dollars for 31 days