Question

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.
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:
\[
a_n = 4 \cdot (1)n-1
\]