Geometric

Geometric

Application

Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day, etc. If the daily wage continues to double, what is your total income for working 31 days?

Step 1. Write a geometric sequence to represent the situation.

1, 2, 4, 8, 16 …

Step 2. Determine a1, r and n.
GeoApp1-1, GeoApp1-2 and GeoApp1-3

Step 3. Determine the general formula for the sequence .

GeoApp1-4

GeoApp1-5

Step 4. To find the series, substitute and solve.
GeoApp1-6

GeoApp1-7

GeoAPp1-8

GeoApp1-9

The total pay for 31 days is 2,147,483,647¢ or $21,474,836.47.