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Find the common ratio of the geometric sequence 19,95,475,dots Answer:

Find the common ratio of the geometric sequence 19,95,475,… 19,95,475, \ldots \newlineAnswer:

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Full solution

Q. Find the common ratio of the geometric sequence 19,95,475,… 19,95,475, \ldots \newlineAnswer:
  1. Identify Pattern: Identify the pattern in the sequence to determine if it is geometric.\newlineThe sequence provided is 1919, 9595, 475475, which suggests that each term is a multiple of the previous term. This indicates that the sequence is likely geometric.
  2. Calculate Ratio: Calculate the ratio between the second and the first term to find the common ratio.\newlineThe second term is 9595 and the first term is 1919. To find the common ratio, we divide the second term by the first term.\newlineCommon ratio = 9519\frac{95}{19}
  3. Perform Division: Perform the division to find the common ratio. 9595 divided by 1919 equals 55. Common ratio = 55
  4. Verify Common Ratio: Verify the common ratio by checking if the third term is a product of the second term and the common ratio.\newlineThe third term is 475475 and the second term is 9595. Multiply the second term by the common ratio to see if it equals the third term.\newline95×5=47595 \times 5 = 475\newlineThis confirms that the common ratio is correct.

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