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.

2, -4, 8,
Write your answer using decimals and integers.
an = __ ( __ )^n-1

1 answer

To find the equation describing the sequence 2, -4, 8, we notice that the first term (\(a_1\)) is 2, the second term (\(a_2\)) is -4, and the third term (\(a_3\)) is 8.

We can observe that the common ratio between consecutive terms is -2:

  • \(-4 / 2 = -2\)
  • \(8 / -4 = -2\)

This indicates that the sequence is a geometric sequence with a common ratio of -2.

Now, the general formula for a geometric sequence can be expressed as:

\[ a_n = a_1 \cdot r^{n-1} \]

Where \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the position of the term.

Plugging in the values we have:

  • \(a_1 = 2\)
  • \(r = -2\)

So the equation becomes:

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

Thus, the final answer is:

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