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What is the next term of the geometric sequence? 5,15,45", "

What is the next term of the geometric sequence?\newline5,15,455, 15, 45

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Full solution

Q. What is the next term of the geometric sequence?\newline5,15,455, 15, 45
  1. Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic.\newlineIn the given sequence, each term after the first is obtained by multiplying the previous term by a constant number, which suggests that the sequence is geometric.
  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, or the third term by the second term.\newline155=3\frac{15}{5} = 3\newline4515=3\frac{45}{15} = 3\newlineCommon Ratio: 33
  3. Find Next Term: Find the next term in the sequence.\newlineTo find the next term, multiply the last known term by the common ratio.\newline45×3=13545 \times 3 = 135\newlineNext Term: 135135

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