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 $-1,-2,-4,\dots$, 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:

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