Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.


18 , 36 , 72 , ...


Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

To describe the sequence \(18, 36, 72, \ldots\) with an equation, we first need to identify the pattern in the sequence.

We can observe that:
- The first term is \(18\).
- The second term is \(36\) (which is \(18 \times 2\)).
- The third term is \(72\) (which is \(18 \times 4\)).

Notice that the terms are multiplied by increasing powers of \(2\):
- Term 1: \(18 \times 2^0 = 18\)
- Term 2: \(18 \times 2^1 = 36\)
- Term 3: \(18 \times 2^2 = 72\)

From this, we can see the general formula for the \(n\)-th term of the sequence can be expressed as:
\[
a_n = 18 \times 2^{n-1}
\]

So, the complete equation to describe the sequence is:
\[
a_n = 18 \cdot 2^{n - 1}
\]

Where:
- \(a_n\) represents the \(n\)-th term of the sequence.
- \(n\) is the position in the sequence (starting from \(n = 1\) for the first term).