Write an equation to describe the sequence below.Use n to represent the position of a term in the sequence,where n = 1 for the first term.

Question

1, 4, 16,
Write your answer using decimals and integers.
an = __ ( __ )n-1

Answer 1

The given sequence is: 1, 4, 16.

Let's analyze the terms:

• The first term is \(1\) (which is \(4^0\)),
• The second term is \(4\) (which is \(4^1\)),
• The third term is \(16\) (which is \(4^2\)).

From this, we can observe that the terms can be expressed as powers of \(4\).

The \(n\)-th term of the sequence can be expressed as: \[ a_n = 4^{n-1} \]

In the requested format, using decimals and integers, we can write:

\[ a_n = 4 \times (1)n-1 \]

Thus, the answer is: \[ a_n = 4 \cdot (1)n-1 \]