ANSWER
EXPLANATION
The sum of the first 
terms of a geometric sequence is given by;
Where , is the number of terms and 
is the first term.
When 
, we have 
, we get;
The ratio 1:2 means there are twice as many dimes as there are quarters. An expression could be n=2d, n being number of quarters, d being number of dimes.
I drew a picture for you. It's below ^.^
<u>We are given:</u>
An even number 'n', multiplied by the next consecutive even number is 168
<u>Solving for n:</u>
From the given statement, we can say that:
n(n+2) = 168 [<em>n multiplied by the next even number 'n+2'</em>]
n² + 2n = 168
n² + 2n - 168 = 0 [<em>subtracting 168 from both sides</em>]
We can see that we now have a quadratic equation, solving using splitting the middle term
n² + 14n - 12n - 168 = 0
n(n + 14) -12(n + 14) = 0 <em>[factoring out common terms</em>]
(n-12)(n+14) = 0
Here, we can divide both sides by either (n-12) OR (n+14)
Checking the result in both the cases:
(n + 14) = 0/(n-12) (n-12) = 0/(n+14)
n + 14 = 0 n - 12 = 0
n = -14 n = 12
Both these values are even and since we are not told if the number 'n' is positive or negative, both 12 and -14 are the possible values of n
