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What is the next term of the geometric sequence? -(16)/(5),8,-20", "

What is the next term of the geometric sequence?\newline−165-\frac{16}{5}, 88, −20-20

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Full solution

Q. What is the next term of the geometric sequence?\newline−165-\frac{16}{5}, 88, −20-20
  1. Identify sequence type: Identify the type of sequence.\newlineThe given sequence has terms that are multiplied by a common ratio rr to get from one term to the next. This indicates that it is a geometric sequence.
  2. Determine common ratio: Determine the common ratio rr of the sequence.\newlineTo find the common ratio, divide the second term by the first term: r=8−(165)=8×(−516)=−2.5r = \frac{8}{-(\frac{16}{5})} = 8 \times (-\frac{5}{16}) = -2.5\newlineSimilarly, check the ratio with the third and second term: r=−208=−2.5r = \frac{-20}{8} = -2.5\newlineSince the common ratio is the same for both pairs of terms, the common ratio is confirmed to be −2.5-2.5.
  3. Calculate next term: Calculate the next term in the sequence using the common ratio.\newlineThe next term is found by multiplying the last known term by the common ratio: Next term = −20×(−2.5)=50-20 \times (-2.5) = 50

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