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What is the next term of the geometric sequence? 189,63,21", "

What is the next term of the geometric sequence?\newline189,63,21,…189, 63, 21, \ldots

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Full solution

Q. What is the next term of the geometric sequence?\newline189,63,21,…189, 63, 21, \ldots
  1. Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic.\newlineIn the given sequence, each term is divided by the same number to get the next term.\newlineThe given sequence is geometric.
  2. Find Common Ratio: Identify the common ratio of the sequence.\newlineTo find the common ratio, divide the second term by the first term.\newline63189=13\frac{63}{189} = \frac{1}{3}\newlineCommon Ratio: 13\frac{1}{3}
  3. Find Next Term: Find the next term in the sequence.\newlineTo find the next term, multiply the last known term by the common ratio.\newline21×(13)=721 \times \left(\frac{1}{3}\right) = 7\newlineNext Term: 77

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