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What is the next term of the geometric sequence? 2,6,18", "

What is the next term of the geometric sequence?\newline2,6,182, 6, 18,

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Full solution

Q. What is the next term of the geometric sequence?\newline2,6,182, 6, 18,
  1. Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic.\newlineIn the given sequence, each term after the first is multiplied by a common ratio rr to get the next term. This indicates that the sequence is geometric.
  2. Find Common Ratio: Determine the common ratio of the sequence.\newlineTo find the common ratio, divide the second term by the first term, or the third term by the second term.\newline62=3\frac{6}{2} = 3 and 186=3\frac{18}{6} = 3\newlineCommon Ratio: 33
  3. Calculate Next Term: Calculate the next term in the sequence using the common ratio.\newlineThe last given term is 1818, and the common ratio is 33.\newline18×3=5418 \times 3 = 54\newlineThe next term in the sequence is 5454.

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