![]() ![]() The greatest value in this association is understanding how the ideas are related and how to derive the formulas from fundamental concepts. This also makes it easier to learn and work with the formulas. We treat them together because some obvi- ous parallels between these kinds of sequences lead to similar formulas. Two kinds of regular sequences occur so often that they have specific names, arithmetic and geometric sequences. Thus, the sequence is neither geometric nor arithmetic. There is no common difference, so the sequence is not arithmetic. Since the differences are constant, the sequence is arithmetic. Since the ratios are constant, the sequence is geometric. The common ratio is -1.įind the ratios of the differences of consecutive termsįind the differences of consecutive terms. ![]() The ratios are not constant, so the sequence is not geometric. The sequence 5, 10, 20, 40, 80,…, 5⋅2 ( n-1), …, Where each term after the first is obtained by multiplying the preceding term by 2, is an Example of a geometric sequence.ĭetermine whether each sequence is arithmetic, geometric, or neither. The sequence 5, 7, 9, 11, 13,…, 5+2( n-1), …, where each term after the first is obtained by adding 2 to the preceding term, is an Example of an arithmetic sequence. ![]()
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