Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. Write the formula for this sequence in the form an = a1 ⋅ rn

Question

Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. Write the formula for this sequence in the form an = a1 ⋅ rn−1. Explain how you arrived at your answer.

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Latifah 5 months 2021-08-04T20:21:02+00:00 1 Answers 30 views 0

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    2021-08-04T20:22:09+00:00

    Answer:

    a_n = 4.5 * 3^{n-1}

    Step-by-step explanation:

    Given

    a_4 = 121.5

    r = 3

    Required

    a_n = a_1 * r^{n -1}

    Substitute 4 for n in a_n = a_1 * r^{n -1}

    a_4 = a_1 * r^{4 -1}

    a_4 = a_1 * r^3

    Substitute 121.5 for a_4

    121.5 = a_1 * 3^3

    121.5 = a_1 * 27

    Solve for a1

    a_1 = \frac{121.5}{27}

    a_1 = 4.5

    So, we have:

    a_n = a_1 * r^{n -1}

    a_n = 4.5 * 3^{n-1}

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