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in a geometric sequence the first term is 2. The 3rd term is the sum of the 1st and 2nd term. Find the ratio, and the 2 terms

  • math -

    a = 2
    term(3) = ar^2 = 2r^2
    term(2) = ar = 2r

    2 + 2r = 2r^2
    r^2 - r - 1 = 0
    r = (1 ± √5)/2

    if r = (1 + √5)/2 , which btw, is the GOLDEN RATIO
    the first 2 terms are
    2 and 1 + √5

    if r = (1 - √5)/2
    the first 2 terms are
    2 and 1 - √5

    check: using my calculator and decimals

    terms are 2 , 3.236.. , 5.236..
    the third time is the sum of the first two

    or

    terms are 2, -1.236.. , .7639...
    .7639 = 2 - 1.236 , ok

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