Sequences and Series (003)

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Sequences and Series (003)
The first term of a geometric progreesion is 10 and its sum to infinity is 15.Find the third term of the progression.

Solution:  ∵geometric progreesion formula is S=a(1-q^n)/1-q. a is first term,q is
common ratio, n is term.
But in this question  "its sum to infinity is 15",
So （见图片）
∴ S=a/(1-q)
15=10/(1-q)
So q=-1/2
所以a3=aq^2
      =10×（-1、2）^2
      5/2

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