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What is the next term of the geometric sequence? (40)/(27),(20)/(9),(10)/(3)", "

What is the next term of the geometric sequence? \newline4027\frac{40}{27}, 209\frac{20}{9}, 103\frac{10}{3}

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Full solution

Q. What is the next term of the geometric sequence? \newline4027\frac{40}{27}, 209\frac{20}{9}, 103\frac{10}{3}
  1. Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic.\newlineThe given sequence has terms that are each a constant factor of the previous term, which indicates that it is a geometric sequence.
  2. Find Common Ratio: Identify the common ratio of the geometric sequence.\newlineTo find the common ratio, divide the second term by the first term.\newlineCommon Ratio rr = 209\frac{20}{9} / 4027\frac{40}{27} = 209\frac{20}{9} * 2740\frac{27}{40} = 21\frac{2}{1} * 34\frac{3}{4} = 64\frac{6}{4} = 32\frac{3}{2}
  3. Calculate Next Term: Find the next term in the sequence using the common ratio.\newlineThe last term given in the sequence is (10/3)(10/3). To find the next term, multiply the last term by the common ratio.\newlineNext Term = (10/3)×(3/2)=(10/1)×(1/2)=10/2=5(10/3) \times (3/2) = (10/1) \times (1/2) = 10/2 = 5

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