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What is the next term of the geometric sequence? 7,21,63", "

What is the next term of the geometric sequence?\newline7,21,637, 21, 63,

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Full solution

Q. What is the next term of the geometric sequence?\newline7,21,637, 21, 63,
  1. Identify pattern in sequence: Identify the pattern in the sequence to determine if it is geometric.\newlineThe sequence is 77, 2121, 6363. Each term is obtained by multiplying the previous term by a constant number.
  2. Calculate common ratio: Calculate the common ratio of the sequence.\newlineThe second term is 2121 and the first term is 77. To find the common ratio, divide the second term by the first term: 217=3\frac{21}{7} = 3.\newlineThe third term is 6363 and the second term is 2121. To confirm the common ratio, divide the third term by the second term: 6321=3\frac{63}{21} = 3.\newlineThe common ratio is confirmed to be 33.
  3. Find next term in sequence: Find the next term in the sequence by multiplying the last known term by the common ratio.\newlineThe last known term is 6363, and the common ratio is 33. Multiply these to find the next term: 63×3=18963 \times 3 = 189.

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