Question
Use the recursively defined geometric sequence \( a_{1}=\frac{5}{6}, a_{n}=4 a_{n-1} \) and find the common ratio. (1 point) \( 0 \frac{5}{6} \) \( 0-\frac{2}{3} \) \( 0 \frac{10}{3} \)
Ask by Guzman Hardy. in the United States
Dec 27,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The common ratio is 4.
Solution
The common ratio \( r \) of a geometric sequence defined recursively by \( a_n = 4a_{n-1} \) is:
\[ r = 4 \]
It appears that the provided options may contain a typographical error, as the correct common ratio is **4**.
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Simplify this solution The Deep Dive
In a geometric sequence, the common ratio \( r \) can be determined using the formula for the sequence. Here, we see that each term is generated by multiplying the previous term by 4. Therefore, the common ratio \( r \) for this sequence is simply 4. So, regardless of the initial term \( a_1 = \frac{5}{6} \), the common ratio remains the same: \( r = 4 \). That means each term is 4 times the one before it, and that ratio does not change throughout the sequence!
