The sum of the first two terms of a geometric series is 4. The sum of the first four terms of the same series is 40. Determine the first five terms of the series.

I am having trouble finding the r value.

I know that $a= 4/(1+r)$

But, im not sure what equation to sub this into to find the r value.


Suppose that the common ratio is $r$ and the first term is $a$; then all terms are of the form $a \cdot r^n$ for $n = 0, 1, 2, \dots$. Then you can get an equation from the first statement:

$$a + ar = 4$$

and from the second statement:

$$a + ar + ar^2 + ar^3 = 40$$

So you have two equations and two variables. In order to solve this, perhaps group the second equation as

$$40 = a + ar + r^2 (a + ar) = 4 + 4r^2$$


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