Question

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

Answer 1

Answer:

Step-by-step explanation:

Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year. This means that for each year, her income is 104% of the previous year. So the rate of increase is 104/100 = 1.04. This rate is in geometric progression. The formula for the sum of n terms of a geometric sequence is expressed as

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

Where

Sn is the nth term

a is the first term

n is the number of terms.

r is the rate or common ratio

From the information given,

a = 33000

r = 1.04

The formula for Alexis total earning over n years will be

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

Her earnings for the next 15 years would be

S15 = 33000(1.04^15 - 1)/(1.04 - 1)

S15 = 33000(0.8009) / 0.04

S15 = $668167.50