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22 August, 16:59

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.

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  1. 22 August, 20:26
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    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
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