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

1 answer

To find an equation that describes the sequence 1,2,4,, we first need to analyze the pattern.

  1. Identify the pattern:

    • The sequence can be seen as:
      • a1=1
      • a2=2
      • a3=4
  2. Determine the relationship:

    • The first term is 1.
    • The second term is 2 which can be viewed as 1×21.
    • The third term is 4 which can be viewed as 1×22.

    We can see that:

    • an=1×2n1.
  3. Write the equation: Therefore, the equation that describes the sequence is:

an=1(2)n1

So, you would fill in the blanks as follows:

an=1(2)n1