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What is the next term of the geometric sequence? -(1)/(7),(4)/(7),-(16)/(7)", "

What is the next term of the geometric sequence?\newline−17-\frac{1}{7}, 47\frac{4}{7}, −167-\frac{16}{7}

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Full solution

Q. What is the next term of the geometric sequence?\newline−17-\frac{1}{7}, 47\frac{4}{7}, −167-\frac{16}{7}
  1. Identify pattern in sequence: Identify the pattern in the sequence to determine if it is geometric.\newlineThe sequence is given as: −(17)-(\frac{1}{7}), (47)(\frac{4}{7}), −(167)-(\frac{16}{7})\newlineWe can see that each term is obtained by multiplying the previous term by a common ratio.
  2. Find common ratio: Find the common ratio by dividing the second term by the first term.\newlineCommon ratio rr = 47\frac{4}{7} / −(1)7\frac{-(1)}{7} = −4-4
  3. Verify common ratio: Verify the common ratio by dividing the third term by the second term to ensure consistency.\newlineCheck ratio = (−167)÷(47)=−4\left(-\frac{16}{7}\right) \div \left(\frac{4}{7}\right) = -4\newlineThe common ratio is consistent, confirming that the sequence is geometric with a common ratio of −4-4.
  4. Calculate next term: Calculate the next term by multiplying the last known term by the common ratio.\newlineNext term = −(167)×−4=647-(\frac{16}{7}) \times -4 = \frac{64}{7}

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