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, –2, –4, ...
Write your answer using decimals and integers.
an = ____ (___)^n-1

Answer 1

To find an equation that describes the sequence \(-1, -2, -4, \ldots\), we first need to analyze the pattern.

1. Identify the pattern:

   • The sequence can be seen as:
     • \(a_1 = -1\)
     • \(a_2 = -2\)
     • \(a_3 = -4\)

2. Determine the relationship:

   • The first term is \(-1\).
   • The second term is \(-2\) which can be viewed as \(-1 \times 2^1\).
   • The third term is \(-4\) which can be viewed as \(-1 \times 2^2\).

   We can see that:

   • \(a_n = -1 \times 2^{n-1}\).

3. Write the equation: Therefore, the equation that describes the sequence is:

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

So, you would fill in the blanks as follows:

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