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: \(\frac{18}{5}, \frac{6}{5}, \frac{2}{5}, \frac{2}{15}, \ldots\)
Recall that the common ratio \(r\) in a geometric sequence is found by dividing any term by the previous term, i.e., \(r = \frac{a_{n+1}}{a_n}\).
Calculate the ratio between the second term and the first term: \(r = \frac{\frac{6}{5}}{\frac{18}{5}}\).
Simplify the division of fractions by multiplying the numerator by the reciprocal of the denominator: \(r = \frac{6}{5} \times \frac{5}{18}\).
Simplify the resulting expression by canceling common factors to find the common ratio \(r\).
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