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:
\[ a_n = 9n + 6 \]
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