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What is the next term of the geometric sequence? 2,-10,50", "

What is the next term of the geometric sequence?\newline2,−10,502,-10,50

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Full solution

Q. What is the next term of the geometric sequence?\newline2,−10,502,-10,50
  1. Identify pattern of sequence: Identify the pattern of the sequence.\newlineThe given sequence is 2,−10,502, -10, 50. We need to determine if this is a geometric sequence by finding a common ratio.
  2. Calculate common ratio: Calculate the common ratio.\newlineTo find the common ratio, we divide the second term by the first term and the third term by the second term.\newlineCommon ratio rr = −10-10 / 22 = −5-5\newlineCheck with the next term: 5050 / −10-10 = −5-5\newlineThe common ratio is consistent, so the sequence is geometric with a common ratio of −5-5.
  3. Find next term in sequence: Find the next term in the sequence.\newlineTo find the next term, we multiply the last known term by the common ratio.\newlineNext term = 50×(−5)=−25050 \times (-5) = -250

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