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Functions 11: Series and Sequence 2

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The sum of the first two terms of a geometric sequence is 3. The sum of the next two terms is 4/3. Find the first four terms of the sequence.

  • Functions 11: Series and Sequence 2 - ,

    Let the four terms be a,b,c,d, and be the common ratio.

    b=ar
    c=ar²
    d=ar³

    a+b=a(1+r)=3
    c+d=ar²(1+r)=4/3

    (c+d)/(a+b) = r² = (4/3)/3=4/9
    =>
    r=√(4/9)=±2/3, assume 2/3

    a+b=a(1+r)=a(1+2/3)=5a/3=3
    =>
    a=9/5
    b=ar=6/5
    c=ar²=4/5
    d=ar³=8/15

  • Functions 11: Series and Sequence 2 - ,

    Thanks a lot:)

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