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What is the next term of the geometric sequence? 20,-10,5", "

What is the next term of the geometric sequence?\newline20,−10,5,20, -10, 5,

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Full solution

Q. What is the next term of the geometric sequence?\newline20,−10,5,20, -10, 5,
  1. Identify sequence type: Identify the type of sequence.\newlineThe given sequence is 2020, −10-10, 55, which changes sign and magnitude. This indicates that it is a geometric sequence because each term is multiplied by a common ratio to get the next term.
  2. Determine common ratio: Determine the common ratio of the sequence.\newlineTo find the common ratio, divide the second term by the first term: −1020=−12-\frac{10}{20} = -\frac{1}{2}. Then, check this ratio by dividing the third term by the second term: 5−10=−12\frac{5}{-10} = -\frac{1}{2}. Since the ratio is consistent, the common ratio is −12-\frac{1}{2}.
  3. Calculate next term: Calculate the next term in the sequence.\newlineTo find the next term, multiply the last known term by the common ratio: 5×(−12)=−2.55 \times \left(-\frac{1}{2}\right) = -2.5.

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