# Another Geometric Series Question.

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• April 10th 2009, 12:30 PM
db5vry
Another Geometric Series Question.
A geometric series has first term a and common ratio r. The sum of the first two terms of the geometric series is 7.2. The sum to infinity of the series is 20. Given that r is positive, find the values of r and a. [6]

First I look at the sum to infinity and see that 20 - 20r = a

And then I put 7.2 = $\frac{a (1 - r^2)}{(1 - r)}$
And subbing what I worked out above, $\frac{20 - 20r (1 - r^2)}{(1 - r)}$

And then I end up with 7.2 = $\frac{20 - 20r - 20r^2 - 20r^3}{(1 - r)}$

• April 10th 2009, 01:11 PM
stapel
I think you're on the right track, but you maybe went slightly askew.... (Blush)

From the formula for the sum of a geometric series, you have arrived at $a\, =\, 20\, -\, 20r$, where $a$ is the first term of the series.

Now use the fact that the second term is $ar$:

. . . . . $20\, -\, 20r + (20\, -\, 20r)r\, =\, 20\, -\, 20r^2\, =\, 7.2$

Solve by square roots. (Wink)
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