Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.

8 , 16 , 32 , ...

Write your answer using decimals and integers.

an =
(
)n - 1

1 answer

To describe the sequence 8, 16, 32, ..., we first observe that each term is double the previous term. This shows that the sequence is geometric.

The first term \( a_1 = 8 \) and the common ratio \( r = 2 \).

The general formula for the \( n \)-th term of a geometric sequence is given by:

\[ a_n = a_1 \cdot r^{(n-1)} \]

Substituting \( a_1 \) with 8 and \( r \) with 2, we have:

\[ a_n = 8 \cdot 2^{(n-1)} \]

Thus, the equation to describe the sequence is:

\[ a_n = 8 \cdot 2^{(n-1)} \]