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

To describe the sequence \( 1, 4, 16, \ldots \), we can analyze the terms in relation to their position \( n \):

- For \( n = 1 \): \( a_1 = 1 \)
- For \( n = 2 \): \( a_2 = 4 \)
- For \( n = 3 \): \( a_3 = 16 \)

We can see that the terms are powers of 4:
- \( 1 = 4^0 \)
- \( 4 = 4^1 \)
- \( 16 = 4^2 \)

This indicates that each term can be expressed as \( a_n = 4^{n-1} \).

Thus, the equation to describe the sequence is:

\[
a_n = 4^{n-1}
\]