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In an arithmetic sequence the sum of the first 15 terms is 615 and the 13th term is six times the second. Find the first three terms.

Geometric Progression

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  1. "the 13th term is six times the second" ---> a + 12d = 6(a+d)
    a + 12d = 6a + 6d
    6d = 5a
    d = 5a/6
    "the sum of the first 15 terms is 615"
    ---> (15/2)(2a + 14d) = 615
    2a + 14d = 82
    a + 7d = 41
    use substitution:
    a + 7(5a/6)= 41
    6a + 35a = 246
    41a = 246
    a = 6 , then d = 5/6 (6) = 5

    so you have 6 , 11, 16, ...

    No idea what the "Geometric Progression" comment at the end of
    your post is supposed to mean.

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