Math

a geometric progression has a third term of 20 and a sum to infinity which is three times the first term. find the first term

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  1. Is this a follow up from your previous question?

    term(3) = ar^2 = 20
    a = 20/r^2

    a/(1-r) = 3a
    1/(1-r) = 3
    same as in your previous post, r = 2/3

    then a = 20/(4/9(
    = 20(9/4) = 45

    test:
    your sequence is 45 , 30 , 20 , 40/3 , 80/9 , ...
    is the third term 20 ? , YES
    sum of all terms = 20/(1-2/3)
    = 20/(1/3)
    = 60 , which is 3 times the first term.
    All is good!

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