SOLUTION: find the sum of the first n terms of the G.P 5+15+45+......... what is the smallest number of terms that will give a total of 1000.

Question 1083649: find the sum of the first n terms of the G.P 5+15+45+......... what is the smallest number of terms that will give a total of 1000.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The first term is .
The common ratio is r=15�5=3 .
Term number is .
The sum of the first terms is

If we want to find what is the smallest n
that will make the,sun of the first n terms no less than 100, our inequality is

The sum of first terms that is no less than 1000 is the sum of the first 6 terms:
5+15+45+135+405+1215.
The sum of some terms cannot be exactly 1000.
For the sum of some terms of the form
(with being some integer)
to be exactly 1000,
the sum of all the factors has to be 200.�
All those factors are multiples of 3, except .
and the sum of multiples of 3 cannot be either 200 or 199.
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