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What kind of sequence is this?\newline15,30,60,120,…15, 30, 60, 120, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Q. What kind of sequence is this?\newline15,30,60,120,…15, 30, 60, 120, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 15,30,60,120,…15, 30, 60, 120, \ldots\newlineAre the consecutive differences in the sequence equal? Let's calculate:\newline30−15=1530 - 15 = 15,\newline60−30=3060 - 30 = 30,\newline120−60=60120 - 60 = 60.\newlineThe consecutive differences in the sequence are not equal.
  2. Check Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 15,30,60,120,…15, 30, 60, 120, \ldots\newlineAre the ratios between consecutive terms in the sequence equal? Let's calculate:\newline3015=2\frac{30}{15} = 2,\newline6030=2\frac{60}{30} = 2,\newline12060=2\frac{120}{60} = 2.\newlineYes, the sequence has a common ratio of 22.
  3. Sequence Type Conclusion: Based on the calculations:\newline- An arithmetic sequence has a common difference between consecutive terms.\newline- A geometric sequence has a common ratio between consecutive terms.\newlineSince the given sequence has no common difference but has a common ratio, it is a geometric sequence.

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