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Write the next three terms of the geometric sequence 243,-81,27,-9, ... _____

Write the next three terms of the geometric sequence 243,−81,27,−9,…243,-81,27,-9,\dots\newline_____

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Full solution

Q. Write the next three terms of the geometric sequence 243,−81,27,−9,…243,-81,27,-9,\dots\newline_____
  1. Identify common ratio: Identify the common ratio by dividing the second term by the first term.\newlineCalculation: (−81)÷243=−13(-81) \div 243 = -\frac{1}{3}
  2. Find next term: Use the common ratio to find the next term after −9-9.\newlineCalculation: −9×(−13)=3-9 \times (-\frac{1}{3}) = 3
  3. Continue using ratio: Continue using the common ratio to find the subsequent term.\newlineCalculation: 3×(−13)=−13 \times (-\frac{1}{3}) = -1
  4. Find subsequent term: Find the next term using the same common ratio.\newlineCalculation: −1×(−13)=13-1 \times \left(-\frac{1}{3}\right) = \frac{1}{3}

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