Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.

18 , 36 , 72 , ...

Write your answer using decimals and integers.

an =
(
)n - 1

1 answer

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).