Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.
2 , 4 , 8 , ...
Write your answer using decimals and integers.

an = _(_)^ n^ -^ 1

Answer 1

To describe the given sequence \(2, 4, 8, \ldots\) using the position \(n\) of the term, we first identify the pattern.

The sequence starts at \(2\) and each subsequent term is doubled:

- The 1st term (\(n=1\)) is \(2\),
- The 2nd term (\(n=2\)) is \(4\),
- The 3rd term (\(n=3\)) is \(8\).

We can see that each term is \(2\) raised to a power, specifically:

- The 1st term: \(2^1\),
- The 2nd term: \(2^2\),
- The 3rd term: \(2^3\).

Thus, for the \(n\)th term, we have the general formula:

\[
a_n = 2^n
\]

Since you requested to format it in a specific way, we can rewrite it to match the requested form:

\[
a_n = (2)^n - 1
\]

However, note that this expression includes an incorrect subtraction. The correct way to express the formula is simply:

\[
a_n = 2^n
\]

To stick closely to your template as best as possible, we can state it as:

\[
a_n = (2)^n
\]

But the first term \(2^n\) correctly represents the sequence without any need for subtraction.