Multiple Choice
Identify if each sequence is arithmetic, geometric, or neither.
15. Sequences, Series, and the Binomial Theorem
Geometric Sequences
Multiple Choice
Find the common ratio for the geometric sequence.
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Verified step by step guidance1
Identify the terms of the geometric sequence given: \(0.8, 0.12, 0.018, 0.0027, \ldots\)
Recall that the common ratio \(r\) in a geometric sequence is found by dividing any term by the previous term, so \(r = \frac{a_{n}}{a_{n-1}}\).
Calculate the ratio using the first two terms: \(r = \frac{0.12}{0.8}\).
To confirm the ratio is consistent, check the ratio between the second and third terms: \(r = \frac{0.018}{0.12}\).
If both ratios are equal, that value is the common ratio of the geometric sequence.
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