To find an equation that describes the given sequence (15, 30, 60, ...), let's analyze the terms and look for a pattern.
- The first term \(a_1 = 15\).
- The second term \(a_2 = 30\).
- The third term \(a_3 = 60\).
Observing the terms:
- \(a_2 = 2 \times a_1 = 2 \times 15 = 30\)
- \(a_3 = 2 \times a_2 = 2 \times 30 = 60\)
It appears that each term is a multiple of 15:
- \(a_1 = 15 \times 1\)
- \(a_2 = 15 \times 2\)
- \(a_3 = 15 \times 4\)
The pattern suggests that the terms can be written in the form of powers of 2 multiplied by 15. Specifically:
- The sequence can be rewritten as:
- \(a_n = 15 \times 2^{n-1}\)
Putting this into the format you're looking for:
\[ a_n = 15 \times 2^{n - 1} \]
Thus, the equation that describes the sequence is:
\[ a_n = 15 \cdot 2^{n - 1} \]