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10 December, 09:15

The common difference, d in an arithmetic sequence whose fourth term is 16 and whose seventh therm is 31

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  1. 10 December, 09:19
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    Answer: d=5

    Step-by-step explanation:

    Arithmetic progression

    An=a1+d (n-1)

    An = nth term

    A1 = first term

    D = common difference

    N = nth position

    We are given the 4th and 7th terms

    For 4th term, n=4

    A4=a1+d (4-1)

    A4 = 16

    16 = a1+d (4-1)

    16 = a1+3d ... equation 1

    For the 7th term, n=7

    A7=a1+d (7-1)

    A7 = 31

    31=a1+6d ... equation 2

    Bring them together

    16=a1+3d

    31=a1+6d

    Subtract equation 1 from 2

    So we have

    15=3d

    D=15/3

    D=5

    Therefore, the common difference is 5
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