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28 January, 20:16

The 6th term is 22 and the common difference is 6. what is the 50th term

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  1. 28 January, 20:52
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    The general formula for an arithmetic sequence is:

    a (n) = a + d (n - 1)

    a : first term

    d : common difference (6)

    n : number of the term

    In your example, you are told the 6th term is 22.

    a (6) = a + 6 (6 - 1) = 22

    a + 30 = 22

    a = 22 - 30

    a = - 8

    So now you have the general formula:

    a (n) = - 8 + 6 (n - 1)

    If you like you can simplify it:

    a (n) = - 8 + 6n - 6

    a (n) = 6n - 14

    Then you can plug in n = 50:

    a (50) = 6 (50) - 14

    = 300 - 14

    = 286
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