Find a1, for the given geometric series. Round to the nearest hundredth if necessary. Sn= 86,830, r= 2.2, n=4

Question

Find a1, for the given geometric series. Round to the nearest hundredth if necessary. Sn= 86,830, r= 2.2, n=4

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Elliana 4 days 2021-10-09T19:31:20+00:00 1 Answer 0

Answers ( )

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    2021-10-09T19:33:12+00:00

    Answer:

    4,646.30

    Step-by-step explanation:

    The sum of n terms of geometric sequence can be calculated using formula

    S_n=\dfrac{a_1(1-r^n)}{1-r}

    In your case,

    S_n=86,830\\ \\r=2.2\\ \\n=4\\ \\a_1=?

    Substitute into the formula:

    S_4=\dfrac{a_1(1-2.2^4)}{1-2.2}\\ \\86,830=\dfrac{a_1(1-23.4256)}{-1.2}\\ \\-104,196=a_1(-22.4256)\\ \\22.4256a_1=104,196\\ \\a_1=\dfrac{104,196}{22.4256}\approx 4,646.30

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