Question
Find the common ratio of the geometric sequence
Answer Attempt 1 out of 3
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In a geometric sequence, the common ratio can be found by dividing any term by the term that precedes it. Here, we can take the second term, -44, and divide it by the first term, -11. This gives us:

To double-check, we can take the third term, -176, and divide it by the second term, -44:

Thus, the common ratio of the sequence is indeed .

When using geometric sequences in the real world, they can be found in various contexts like finance, where compound interest operates on a geometric progression. For instance, if you invest money with a fixed interest rate, every time interest is added, it multiplies the total amount by a certain ratio—akin to climbing up ladder rungs where each step is the previous one multiplied by the same factor!

A common mistake when dealing with geometric sequences is confusing the common ratio with the difference seen in arithmetic sequences. It’s important to remember that in a geometric sequence, you are always multiplying or dividing by the same number (the common ratio) rather than simply adding or subtracting a fixed amount. So if you spot multiplication instead of addition, you’re on the right track!