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What is the next term of the geometric sequence? (81)/(25),(27)/(5),9

What is the next term of the geometric sequence?\newline(8125),(275),9(\frac{81}{25}),(\frac{27}{5}),9

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Full solution

Q. What is the next term of the geometric sequence?\newline(8125),(275),9(\frac{81}{25}),(\frac{27}{5}),9
  1. Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic.\newlineIn the given sequence, consecutive terms seem to have a common ratio rr.\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.\newline(275)/(8125)=(275)⋅(2581)=(27⋅255⋅81)=(33⋅525⋅34)=53(\frac{27}{5}) / (\frac{81}{25}) = (\frac{27}{5}) \cdot (\frac{25}{81}) = (\frac{27\cdot25}{5\cdot81}) = (\frac{3^3\cdot5^2}{5\cdot3^4}) = \frac{5}{3}\newlineCommon Ratio: 53\frac{5}{3}
  3. Find Next Term: Find the next term in the sequence using the common ratio.\newlineThe last term given in the sequence is 99.\newlineTo find the next term, multiply the last term by the common ratio.\newline9×(53)=(91)×(53)=(3×3)×(53)=3×5=159 \times \left(\frac{5}{3}\right) = \left(\frac{9}{1}\right) \times \left(\frac{5}{3}\right) = \left(3\times3\right) \times \left(\frac{5}{3}\right) = 3 \times 5 = 15\newlineNext Term: 1515

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