Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.


7 , 14 , 28 , ...


Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

To find the equation that describes the given sequence \(7, 14, 28, ...\), we first need to identify the pattern or rule governing the sequence.

1. **Identify the pattern**:
- The sequence starts at 7.
- The second term is \(14\) which is \(7 \times 2\).
- The third term \(28\) is \(7 \times 4\), which can also be expressed as \(7 \times 2^2\).

Observing the values, we notice that each term can be expressed as:
- 1st term: \(7 \times 1 = 7\)
- 2nd term: \(7 \times 2 = 14\)
- 3rd term: \(7 \times 4 = 28\)

The multipliers \(1, 2, 4\) are \(2^{(n-1)}\) for \(n = 1, 2, 3\).

2. **Write the equation**:
The nth term of the sequence can be expressed as:
\[
a_n = 7 \times 2^{(n-1)}
\]

Thus, the final equation describing the sequence is:
\[
a_n = 7 \times 2^{(n-1)}
\]