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What is the next term of the geometric sequence? -(3)/(5),(6)/(5),-(12)/(5)", "

What is the next term of the geometric sequence?\newline−35,65,−125-\frac{3}{5}, \frac{6}{5}, -\frac{12}{5},

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Full solution

Q. What is the next term of the geometric sequence?\newline−35,65,−125-\frac{3}{5}, \frac{6}{5}, -\frac{12}{5},
  1. Identify pattern of sequence: Identify the pattern of the given geometric sequence.\newlineThe given sequence is: −(35)-(\frac{3}{5}), (65)(\frac{6}{5}), −(125)-(\frac{12}{5})\newlineWe need to determine if there is a common ratio between the terms.
  2. Calculate common ratio: Calculate the common ratio by dividing the second term by the first term.\newline(65)/(−(35))=−2(\frac{6}{5}) / (-(\frac{3}{5})) = -2\newlineCommon Ratio: −2-2
  3. Verify common ratio: Verify the common ratio by dividing the third term by the second term.\newline−(125)/(65)=−2-\left(\frac{12}{5}\right) / \left(\frac{6}{5}\right) = -2\newlineThe common ratio is consistent.
  4. Find next term: Find the next term by multiplying the last known term by the common ratio.\newlineLast known term: −(125)-(\frac{12}{5})\newlineCommon ratio: −2-2\newlineNext term: −(125)⋅−2=245-(\frac{12}{5}) \cdot -2 = \frac{24}{5}

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