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28 October, 07:40

A geometric sequence is defined by the explicit formula an = 5 (-4) n-1. What is the recursive formula for the nth term of this sequence?

A. an = - 5an-1

B. an+1 = 4an

C. an+1 = 5an

D. an = - 4an-1

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Answers (1)
  1. 28 October, 10:19
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    An = 5 (-4) ^ (n - 1)

    an + 1 = 5 (-4) ^ (n + 1 - 1) = 5 (-4) ^n

    an = 5 (-4) ^ (n - 1) = 5 (-4) ^n / (-4) = an + 1 / (-4)

    an + 1 = - 4an

    an + 1 - 1 = - 4 an - 1

    an = - 4an - 1
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