# Math Help - Another Geometric Series Question.

1. ## 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 = $\frac{20 - 20r - 20r^2 - 20r^3}{(1 - r)}$

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