Question
Determine if the given sequence is geometric. If the sequence is geometric, find the common ratio. \( 4,8,16,32 \ldots \)
Ask by Hart Barrett. in the United States
Feb 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The sequence is geometric with a common ratio of 2.
Solution
A geometric sequence is one in which each term after the first is found by multiplying the previous term by a constant value called the common ratio (r).
For the given sequence: 4, 8, 16, 32, ...
Step 1: Find the ratio between the second term and the first term:
r = 8/4 = 2
Step 2: Verify the ratio for the subsequent terms:
16/8 = 2 and 32/16 = 2
Since the ratio remains constant, the sequence is geometric with a common ratio of 2.
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Simplify this solution The Deep Dive
To check if the sequence \( 4, 8, 16, 32, \ldots \) is geometric, we need to look at the ratios of consecutive terms. To find the common ratio, we divide each term by the previous term: - \( \frac{8}{4} = 2 \) - \( \frac{16}{8} = 2 \) - \( \frac{32}{16} = 2 \) Since the ratio is consistently \( 2 \) for all pairs of consecutive terms, the sequence is indeed geometric with a common ratio of \( 2 \).
