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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

User Dave Chen
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Answer:

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

User Remdezx
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