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14 October, 11:46

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

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  1. 14 October, 12:10
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    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
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