Question

What is a formula for the nth term of the given sequence?
15, comma, 24, comma, 33, point, point, .
15,24,33...

Answer 1

To find the formula for the nth term of the sequence 15, 24, 33, ..., we first look at the differences between consecutive terms:

- \(24 - 15 = 9\)
- \(33 - 24 = 9\)

The difference is consistent, indicating this is an arithmetic sequence, where the common difference \(d = 9\).

The general formula for the nth term of an arithmetic sequence is given by:

\[
a_n = a_1 + (n-1) \cdot d
\]

where:
- \(a_n\) is the nth term,
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.

In this case:
- \(a_1 = 15\)
- \(d = 9\)

Now substituting these values into the formula:

\[
a_n = 15 + (n-1) \cdot 9
\]

Simplifying this gives:

\[
a_n = 15 + 9n - 9
\]
\[
a_n = 9n + 6
\]

Therefore, the formula for the nth term of the sequence is:

\[
a_n = 9n + 6
\]