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math sequences and series

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how do i solve the sum of the first two terms of an arithmetic sequence is 16. the sum of the second and third term is 28. determine the first three terms, algebraically

  • math sequences and series -

    a1 + a2 = 16

    a2 + a3 = 28

    and since it is an arithmetic sequence
    a2 - a1 = a3 - a2
    a2 = (a1+a3)/2 (the average of course)

    substitute back
    a1 + (a1+a3)/2 = 16
    (a1+a3)/2 + a3 = 28

    solve those two equations for a1 and a3, then go back and get a2

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