To identify the type of sequence for the numbers 15, 45, 135, 405, let's analyze the ratios between consecutive terms.
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The ratio of the second term to the first term: \[ \frac{45}{15} = 3 \]
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The ratio of the third term to the second term: \[ \frac{135}{45} = 3 \]
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The ratio of the fourth term to the third term: \[ \frac{405}{135} = 3 \]
Since each term is obtained by multiplying the previous term by 3, this sequence is a geometric sequence. The first term is 15, and the common ratio is 3.
To summarize, the sequence is a geometric sequence where:
- First term (a) = 15
- Common ratio (r) = 3
Thus, the \( n \)-th term of this sequence can be expressed as: \[ a_n = 15 \times 3^{(n-1)} \]