Question

A worker is paid $0.03 on the first day, $0.06 on the second day, $0.12 on the third day, $0.24 on the fourth day, and so on. How much money (rounded to the nearest cent) in total does the worker earn after working 24 days? Hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio.

Answer 1

$503 316.45

Explanation:

Answer 2

The first term a1=$0.03
The common ratio r = a2 : a1 = $0.06 : $0.03 = 2


`S_n = (a_1(1 - r^n))/(1 - r) \\ \\ S_(24)= (0.03(1 - 2^(24)))/(1 - 2) =-0.03(1 - 16777216) =503316.45`

The worker earns after working 24 days $503 316.45