Math

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In an arithmetic sequence, the first term is 5, and the fifth term is 21. What is the second term? Help please ASAP!!

  • Math -

    If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

    an = a1 + ( n - 1 ) * d


    In this case:

    a1 = 5

    n = 5

    a5 = 21


    an = a1 + ( n - 1 ) * d

    a5 = a1 + ( 5 - 1 ) * d

    21 = 5 + 4 * d

    21 - 5 = 4 d

    16 = 4 d Divide both sides with 4

    16 / 4 = 4 d / 4

    4 = d

    d = 4


    a2 = a1 + d

    a2 = 5 + 4

    a2 = 9

  • Math -

    The increase per term is (21 - 5)/(5 - 1)
    = 16/4 = 4

    Add 4 to the first term to get the second term

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