Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
3. Analyzing Geometric Sequences and Series
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Exercise 39 Page 430

We are given two non-consecutive terms of a geometric sequence.
To find the rule for the term, we first need to find the common ratio Let's start by recalling the explicit formula of a geometric sequence.
We will substitute the given information into this formula to write a system of equations. By solving the system, we will find the values of and
To solve the system, we will start by dividing Equation (II) by Equation (I). By doing this, we will eliminate and find the value of
Solve for

We found out that has two possible solutions, and . Knowing the values of , we can substitute them into either of the equations of our system in order to find the value of

First Solution

Let's substitute in Equation (I).
Solve for
Finally, we can write the complete formula for the first solution.

Second Solution

Let's substitute in Equation (I).
Finally, we can write the complete formula for the second solution.