Question

or
Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.


–3 , –6 , –12 , ...


Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

To describe the sequence \(-3, -6, -12, \ldots\), we first need to determine the relationship between the terms in the sequence.

Let's evaluate how we move from one term to the next:

- The first term (when \(n = 1\)) is \(-3\).
- The second term (when \(n = 2\)) is \(-6\).
- The third term (when \(n = 3\)) is \(-12\).

We can observe that each term is being multiplied by a factor of 2 to get the next term:

- \(-3 \times 2 = -6\)
- \(-6 \times 2 = -12\)

This indicates that we have a geometric sequence with:
- First term \(a = -3\)
- Common ratio \(r = 2\)

The general formula for a geometric sequence is given by:
\[
a_n = a \cdot r^{(n-1)}
\]

Substituting \(a = -3\) and \(r = 2\):
\[
a_n = -3 \cdot 2^{(n-1)}
\]

So the equation to describe the sequence is:
\[
a_n = -3 \cdot 2^{(n-1)}
\]
where \(n\) is the position in the sequence, starting from \(n = 1\).