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13 July, 16:30

in a AP the first term is 8, nth term is 33 and sum to first n terms is 123. Find n and common difference

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  1. 13 July, 17:52
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    Step-by-step explanation:

    First I want to set up some variables.

    S = sum

    n = final term

    ax = xth term, so a1 is the first term and an is the last one

    d = common difference.

    There are two formulas to find the sum, if you don't get how they were gotten I'd be happy to explain.

    S = (n/2) (a1+an) = (n/2) (2a1 + (n-1) d)

    So, to find n we use the first one.

    S = (n/2) (a1+an)

    123 = (n/2) (8+33)

    123 = (n/2) 41

    3 = n/2

    6 = n

    Now we can find d with the other one

    S = (n/2) (2a1 + (n-1) d)

    123 = (6/2) (2*8 + (6-1) d)

    123 = 3 (16+5d)

    41 = 16+5d

    25 = 5d

    5 = d

    so there are six terms and the common difference is 5.
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