SOLUTION: Kindly solve and answer this one for me:
the sum of an infinite geometric series is 4 while the sum of all the terms is 192. What are the terms?
thanks
Algebra.Com
Question 983219: Kindly solve and answer this one for me:
the sum of an infinite geometric series is 4 while the sum of all the terms is 192. What are the terms?
thanks
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
Let a be the first term of our geometric progression and r be its common ratio.
Then our first equation is
= .
It is the formula for the sum of infinite geometric progression.
The sequence consisting of cubes of geometric progression is geometric progression itself, with the first term and the common ratio . It is easy to check.
Therefore, the sum of such progression is
= .
It is our second equation.
Now, divide the second equation by the first one. You will get
= .
Thus you decreased the degree of the second equation from 3 to 2.
Next, express the term a from the first equation as
=
and substitute it into the third equation. You will get
= , or
= , or
= .
It is a quadratic equation.
Would you solve it and complete the solution from this point?
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