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Find the common ratio of the geometric sequence -6,36,-216,dots Answer:

Find the common ratio of the geometric sequence −6,36,−216,… -6,36,-216, \ldots \newlineAnswer:

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Full solution

Q. Find the common ratio of the geometric sequence −6,36,−216,… -6,36,-216, \ldots \newlineAnswer:
  1. Divide First Term: To find the common ratio of a geometric sequence, we divide any term by the previous term.\newlineLet's divide the second term by the first term to find the common ratio rr.\newlineCalculation: r=36−6r = \frac{36}{-6}
  2. Calculate Common Ratio: Now, let's perform the division to find the value of rr.\newlineCalculation: r=−6r = -6
  3. Check with Third Term: To ensure that we have the correct common ratio, we should check it by dividing the third term by the second term.\newlineCalculation: r=−21636r = \frac{-216}{36}
  4. Confirm Common Ratio: Perform the division to confirm the common ratio.\newlineCalculation: r=−6r = -6
  5. Final Verification: Since the common ratio calculated from the first and second term is the same as the ratio from the second to the third term, we have found the common ratio correctly.

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