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Find the common ratio of the geometric sequence 18,162,1458,dots Answer:

Find the common ratio of the geometric sequence 18,162,1458,… 18,162,1458, \ldots \newlineAnswer:

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Full solution

Q. Find the common ratio of the geometric sequence 18,162,1458,… 18,162,1458, \ldots \newlineAnswer:
  1. Identify type of sequence: Identify the type of sequence.\newlineThe given sequence is 18,162,1458,…18, 162, 1458, \ldots Since each term is getting larger and appears to be a multiple of the previous term, it suggests that the sequence is geometric.
  2. Calculate common ratio: Calculate the common ratio.\newlineTo find the common ratio, divide the second term by the first term.\newlineCommon ratio rr = 16218\frac{162}{18} = 99
  3. Verify common ratio: Verify the common ratio with the next term.\newlineTo ensure that the common ratio is correct, divide the third term by the second term.\newline1458162=9\frac{1458}{162} = 9\newlineThis confirms that the common ratio is indeed 99.

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