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

12, 24, 48
Write your answer using decimals and integers.
an = __ (__)n-1

Answer 1

To find the equation for the sequence \( 12, 24, 48 \), we first observe the pattern in the terms.

1. The first term is \( 12 \).
2. The second term is \( 24 \), which is \( 12 \times 2 \).
3. The third term is \( 48 \), which is \( 12 \times 4 \).

We can see that each term can be expressed in the form of a constant multiplied by powers of 2:

• The first term \( (n=1) \): \( 12 \times 2^{0} = 12 \)
• The second term \( (n=2) \): \( 12 \times 2^{1} = 24 \)
• The third term \( (n=3) \): \( 12 \times 2^{2} = 48 \)

Thus, we can summarize the pattern as follows:

\[ a_n = 12 \times 2^{n-1} \]

So, the equation to describe the sequence is:

\[ a_n = 12 \times (2)^{n-1} \]

This equation uses integers and shows how each term in the sequence can be generated.