h(1)= 9 h(n)=h(n−1)⋅(-3) Find an explicit formula for h(n). h(n)= ? ​

Question

h(1)= 9

h(n)=h(n−1)⋅(-3)

Find an explicit formula for h(n).

h(n)= ?

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Lệ Thu 7 hours 2021-07-22T17:01:01+00:00 1 Answers 0 views 0

Answers ( )

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    2021-07-22T17:02:02+00:00

    Given:

    h(1)=9

    h(n)=h(n-1)\cdot (-3)

    To find:

    The explicit formula for h(n).

    Solution:

    We have,

    h(n)=h(n-1)\cdot (-3)         …(i)

    It is the recursive formula of a geometric sequence. It is of the form

    a(n)=a(n-1)\cdot r         …(ii)

    where r is the common ratio.

    On comparing (i) and (ii), we get

    r=-3

    We have, h(1)=9 so the first term of the geometric sequence is a=9.

    The explicit formula for a geometric sequence is:

    h(n)=ar^{n-1}

    Substitute a=9 and r=-3 to get the explicit formula for the given sequence.

    h(n)=9(-3)^{n-1}

    Therefore, the required explicit formula is h(n)=9(-3)^{n-1}.

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