Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.

15 , 30 , 60 , ...

Write your answer using decimals and integers.

an =
(
)n - 1

1 answer

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:

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