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What is the next term of the geometric sequence? 54,36,24", "

What is the next term of the geometric sequence?\newline54,36,2454, 36, 24,

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Full solution

Q. What is the next term of the geometric sequence?\newline54,36,2454, 36, 24,
  1. Determine the common ratio: To find the next term of the geometric sequence, we need to determine the common ratio rr of the sequence. The common ratio is found by dividing any term by the previous term.\newlineLet's divide the second term by the first term to find the common ratio.\newliner=3654r = \frac{36}{54}
  2. Perform the division: Now, let's perform the division to find the value of rr.r=3654=23r = \frac{36}{54} = \frac{2}{3}This means that each term is multiplied by 23\frac{2}{3} to get the next term.
  3. Calculate the value of rr: To find the next term after 2424, we multiply 2424 by the common ratio (23)(\frac{2}{3}).\newlineNext term = 24×(23)24 \times (\frac{2}{3})
  4. Multiply by the common ratio: Let's perform the multiplication to find the next term.\newlineNext term = 24×(23)=483=1624 \times \left(\frac{2}{3}\right) = \frac{48}{3} = 16

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