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What kind of sequence is this?\newline6,18,54,162,…6, 18, 54, 162, \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?\newline6,18,54,162,…6, 18, 54, 162, \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: 6,18,54,162,…6, 18, 54, 162, \ldots\newlineAre the consecutive differences in the sequence equal? \newline18−6=1218 - 6 = 12, 54−18=3654 - 18 = 36, 162−54=108162 - 54 = 108.\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: 6,18,54,162,…6, 18, 54, 162, \ldots\newlineAre the ratios between consecutive terms in the sequence equal? \newline186=3,5418=3,16254=3.\frac{18}{6} = 3, \frac{54}{18} = 3, \frac{162}{54} = 3.\newlineYes, the sequence has a common ratio of 33.
  3. Conclusion: Since the sequence does not have a common difference but does have a common ratio, we can conclude that the sequence is not arithmetic but is geometric.

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