SOLUTION: the first three terms of a geometric progression are 100,90 and 81 , the common ratio is 0.9 Find the sum to infinity of its terms ? Can someone explain this step by step p

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Question 1029219: the first three terms of a geometric progression are 100,90 and 81 , the common ratio is 0.9
Find the sum to infinity of its terms ?
Can someone explain this step by step please as I do not understand

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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the first three terms of a geometric progression are 100,90 and 81 , the common ratio is 0.9
Find the sum to infinity of its terms ?
Can someone explain this step by step please as I do not understand
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The sum of the infinite geometric progression with the first term a and the common ratio r is 

a+%2B+ar+%2B+ar%5E2+%2B+ar%5E3+%2B+ellipsis = a%2F%281-r%29,

providing that |r| < 1. 

If you are a school math student, you are not required to understand how this formula is obtained. Simply accept this fact and use this formula.

In your case a = 100 and r = 0.9.
Substitute these values into the formula. You will get

   the infinite sum = 100%2F%281-0.9%29 = 100%2F0.1 = 1000.

That's all. The infinite sum of this geometric progression is 1000.