Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.

7 , 14 , 28 , ...

Write your answer using decimals and integers.

an =
(
)n - 1

1 answer

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: \[ a_n = 7 \times 2^{(n-1)} \]