30 POINTS! Find an explicit formula for the geometric sequence −1,−7,−49,−343 d(n)=

Question

30 POINTS! Find an explicit formula for the geometric sequence −1,−7,−49,−343
d(n)=

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Nem 3 years 2021-09-03T03:12:48+00:00 1 Answers 1 views 0

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  1. minhkhoi
    0
    2021-09-03T03:14:03+00:00
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    Answer:

    d(n) = { - 7}^{n - 1}

    Step-by-step explanation:

    Since the sequence above is a geometric sequence

    For an nth term in a geometric sequence

    d(n) = a ({r})^{n - 1}

    where

    a is the first term

    r is the common ratio

    n is the nth term

    To find the common ratio divide the previous term by the next term

    That’s

    r = \frac{ - 7}{ - 1} = 7 \: \: \: \: or \\ r = \frac{ - 49}{ - 7} = 7 \: \: \: or \\ r = \frac{ - 343}{ - 49} = 7

    So the common ratio / r = 7

    the first term is – 1

    Substitute the values into the above formula

    d(n) = - 1( {7})^{n - 1} \\

    We have the final answer as

    d(n) = { - 7}^{n - 1}

    Hope this helps you

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