A woman made $35,000 during the first year of her new job at city hall. Each year she received a 10% raise. How do you find her total earnings during the first eight years on the job?
Total earnings after 8 years = $400,256.08
Her salary which increases every year forms a geometric sequence.
35,000 ; 38,500 ; 42,350 .......
The common ratio is 1.1. (this can be found by dividing
or by realising that adding 10% onto 100% is the same as multiplying by
We are asked for her total earnings over 8 years. This now represents a geometric series:
35,000 + 38,500 + 42,350 + .......
There is a formula for the sum of the terms: