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AP calculus

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The sixth term of an Arithmetic Progression is 23 and the sum of the six terms is 78. Find the first term and the common difference.

  • AP calculus -

    a+5d = 23
    6/2 * [a + (a+5d)] = 78

    a + 5d = 23
    6a + 15d = 78

    a=3
    d=4

    sequence: 3 7 11 15 19 23
    sum: 78

  • AP calculus -

    Given an arithmetic progression -7,-3,1,..., state three consecutive terms in this progression which sum up to 75.

  • AP calculus -

    The kth term is a+(k-1)d
    so you want

    3a + (k-1 + k + k+1)d = 75

    3(-7) + 3k(4) = 75
    12k = 96
    k=8

    So, the 8th,9th,10th terms are

    21,25,29 add up to 75

  • AP calculus -

    I can already tell that's gonna be super hlepufl.

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