<u>ANSWER</u>
The common ratio is -3.
<u>EXPLANATION</u>
In general, the common ratio of a Geometric Sequence is given by:
We can find the common ratio using any two consecutive terms of the geometric sequence by dividing the subsequent term by the previous term.
The given sequence is -2,6,-18,54
Using the first two terms the common ratio is
We could also used the second and third terms to get
and so on and so forth.
Therefore the common ratio is -3.
For this case, we have the following equation (according to the comments):
First, we factor the quadratic expression in the denominator:
Then, we multiply both sides of the equation by (a-2) (a + 2):
Later, canceling similar terms we have:
We do distributive property on the left side of the equation:
By grouping variables and constant terms we have:
Rewriting we have:
Finally, by clearing "a" we have:
Note: the value of a is a extraneous solution because it makes the denominator of the original equation equal to zero.
Answer:
the student correct, but the value of a= -2 is an extraneous solution