Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.


15 , 30 , 60 , ...


Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

To find an equation that describes the given sequence (15, 30, 60, ...), let's analyze the terms and look for a pattern.

1. The first term \(a_1 = 15\).
2. The second term \(a_2 = 30\).
3. The third term \(a_3 = 60\).

Observing the terms:
- \(a_2 = 2 \times a_1 = 2 \times 15 = 30\)
- \(a_3 = 2 \times a_2 = 2 \times 30 = 60\)

It appears that each term is a multiple of 15:
- \(a_1 = 15 \times 1\)
- \(a_2 = 15 \times 2\)
- \(a_3 = 15 \times 4\)

The pattern suggests that the terms can be written in the form of powers of 2 multiplied by 15. Specifically:

- The sequence can be rewritten as:
- \(a_n = 15 \times 2^{n-1}\)

Putting this into the format you're looking for:

\[
a_n = 15 \times 2^{n - 1}
\]

Thus, the equation that describes the sequence is:

\[
a_n = 15 \cdot 2^{n - 1}
\]