To describe the sequence \(30, 60, 120, \ldots\), we need to identify the pattern and formulate a general equation.
First, let's analyze the sequence. The first term is \(30\), the second term is \(60\), and the third term is \(120\). Observing the relationship between the terms, we can see that:
- \(60 = 30 \times 2\)
- \(120 = 60 \times 2\)
It appears that each term is obtained by multiplying the previous term by 2. However, to find a general term, let's look at how the terms relate to their position \(n\).
Further examination reveals:
- For \(n = 1\): \(a_1 = 30 = 30 \times 2^{0}\)
- For \(n = 2\): \(a_2 = 60 = 30 \times 2^{1}\)
- For \(n = 3\): \(a_3 = 120 = 30 \times 2^{2}\)
From this, we can derive the formula:
\[ a_n = 30 \times 2^{n-1} \]
Thus, the equation to describe the sequence is:
\[ a_n = 30 \times 2^{n-1} \]
1 answer