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29 October, 16:28

The 6th term of an arithmetic progression is 35 and the 13th term is 77. find the 1st term

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  1. 29 October, 16:30
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    Step-by-step explanation:

    The 6th term of an arithmetic progression is 35 and the 13th term is 77. find the 1st term

    We know we have an arithmetic sequence.

    a_n = (n - 1) * d + a_1

    given:

    a_6 = 35 = (6-1) * d + a_1

    a_13 = (13 - 1) * d + a_1 = 77

    find a_1

    we have 35 = 5d + a_1

    and 77 = 12d + a_1

    2 equations in 2 unknowns.

    We can solve this.

    77 = 12d + a_1

    35 = 5d + a_1

    minus the 2 equations from each other.

    77 - 35 = 12d - 5d + a_1 - a_1

    42 = 7d

    d = 6

    Find a_1

    35 = 5*6 + a_1

    35 = 30 + a_1

    a_1 = 35 - 30 = 5

    a_1 = 5
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