Multiple Choice
Write a recursive formula for the geometric sequence .
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20. Sequences, Series & Induction
Geometric Sequences
Multiple Choice
Which of the following sequences is geometric?
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Verified step by step guidance1
Recall that a geometric sequence is one where each term after the first is found by multiplying the previous term by a constant ratio, called the common ratio. Mathematically, this means \(\frac{a_{n+1}}{a_n} = r\) for all \(n\).
For each given sequence, calculate the ratio between consecutive terms. For example, for the sequence \(3, 7, 11, 15, \dots\), compute \(\frac{7}{3}\), \(\frac{11}{7}\), and \(\frac{15}{11}\).
Check if the ratios you calculated for each sequence are the same. If the ratios are equal for all consecutive terms, then the sequence is geometric.
Apply this process to each sequence: \(3, 7, 11, 15, \dots\); \(2, 6, 18, 54, \dots\); \(5, 10, 16, 23, \dots\); and \(1, 4, 9, 16, \dots\).
Identify the sequence where the ratio between consecutive terms remains constant. That sequence is the geometric sequence.
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