an arithmetic sequence “a” starts with 84, 77 define “a” recursively

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an arithmetic sequence “a” starts with 84, 77 define “a” recursively

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Diễm Kiều 1 month 2021-08-04T08:25:44+00:00 1 Answers 8 views 0

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    2021-08-04T08:27:37+00:00

    Answer:

    First, let’s define an arithmetic sequence:

    In an arithmetic sequence, the difference between any two consecutive terms is always the same.

    Then we can write it in a general way as:

    aₙ = a₁ + (n – 1)*d

    where:

    aₙ is the n-th term of the sequence.

    d is the constant difference between two consecutive terms.

    a₁ is the initial term of our sequence.

    Now in this case we know that the first terms of our sequence are:

    84, 77, …

    Then we know the initial term of our sequence:

    a₁ = 84.

    And the value of d can be calculated as:

    d = a₂ – a₁ = 77 – 84 = -7

    Then the general way of writing this sequence is:

    aₙ = 84 + (n – 1)*(-7)

    And the recursion relation is:

    aₙ = aₙ₋₁ – 7

    So for the n-th term, we must subtract 7 of the previous term.

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