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, ...

To analyze the sequence, we can identify the pattern between the terms:

• The first term \( a_1 = 1 = 2^0 \)
• The second term \( a_2 = 4 = 2^2 \)
• The third term \( a_3 = 16 = 2^4 \)

We notice that the exponents are \(0, 2, 4\), which can be described as \(2(n-1)\) where \(n\) is the position of the term in the sequence.

Thus, we can express the nth term \( a_n \) in the following way:

\[ a_n = 2^{2(n-1)} \]

Therefore, the equation describing the sequence is:

\[ a_n = 2^{2(n-1)} \]