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.

-28, -84, -252,
Write your answer using decimals and integers.
an = __ ( __ )^n-1

1 answer

To find the equation for the given sequence \(-28, -84, -252\), we first need to determine whether it's an arithmetic or geometric sequence.

  1. Identify the Sequence Type:

    • Common Ratio: Let's see if this sequence is geometric by calculating the ratio between terms. \[ \frac{-84}{-28} = 3 \] \[ \frac{-252}{-84} = 3 \] Since the ratio between consecutive terms is consistent (both are 3), this is a geometric sequence.
  2. General Form of a Geometric Sequence: The general form of a geometric sequence can be expressed as: \[ a_n = a_1 \cdot r^{(n-1)} \] where \(a_1\) is the first term and \(r\) is the common ratio.

  3. Identify the Constants:

    • The first term \(a_1 = -28\)
    • The common ratio \(r = 3\)
  4. Write the Equation: Now we can substitute these values into the equation: \[ a_n = -28 \cdot (3)^{(n-1)} \]

Thus, the equation for the sequence is: \[ \boxed{a_n = -28 \cdot (3)^{(n-1)}} \]