Question

Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year. Write a geometric series formula, Sn, for Alexa's total earnings over n years. Use this formula to find Alexa's total earnings for her first 15 years of teaching, to the nearest cent.

Answer 1

Answer:

Step-by-step explanation:

The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = [a(r^n) - 1)]/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

a = $33000

r = 1 + 4/100 = 1.04

Therefore, the formula, Sn, for Alexa's total earnings over n years.

Sn = [33000(1.04^n) - 1)]/1.04 - 1

Sn = [3300(1.04^n) - 1)]/0.04

Alexa's total earnings for her first 15 years of teaching would be

S15 = [33000(1.04^15 - 1)]/0.04

S15 = $660778.4 to the nearest cent