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Find the common ratio of the geometric sequence -7,56,-448,dots Answer:

Find the common ratio of the geometric sequence −7,56,−448,… -7,56,-448, \ldots \newlineAnswer:

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Full solution

Q. Find the common ratio of the geometric sequence −7,56,−448,… -7,56,-448, \ldots \newlineAnswer:
  1. Identify sequence type: Identify the type of sequence.\newlineThe given sequence is −7,56,−448,…-7, 56, -448, \ldots Each term seems to be multiplied by a common ratio to obtain the next term, indicating that it is a geometric sequence.
  2. Calculate common ratio: Calculate the common ratio using consecutive terms.\newlineTo find the common ratio, we can divide the second term by the first term.\newlineCommon Ratio rr = 56−7\frac{56}{-7} = −8-8
  3. Verify common ratio: Verify the common ratio with another pair of consecutive terms.\newlineTo ensure that the common ratio is correct, we can also divide the third term by the second term.\newlineCommon Ratio rr = (−448)/56(-448) / 56 = −8-8\newlineThis confirms that the common ratio is consistent across different pairs of terms.

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