Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form.

Question

Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form.

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Thiên Di 5 months 2021-08-10T01:10:44+00:00 1 Answers 16 views 0

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    2021-08-10T01:12:02+00:00

    Answer:

    a_n = -11-14n

    Step-by-step explanation:

    Given

    a_1 = -25

    a_n = a_{n-1}-14

    Required

    The explicit formula

    First, calculate a_2

    Set n=2; So:

    a_2 = a_{2-1}-14

    a_2 = a_{1}-14

    Substitute -25 for a_1

    a_2 = -25-14

    a_2 = -39

    Calculate the common difference (d)

    d = a_2 - a_1

    d = -39 --25

    d = -14

    So, the nth term is:

    a_n = a_1 + (n - 1)d

    a_n = -25+ (n - 1)*-14

    Open bracket

    a_n = -25-14n + 14

    Collect like terms

    a_n = 14-25-14n

    a_n = -11-14n

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )