To write an explicit formula for an arithmetic sequence, we use the formula:
\[ a_n = a_1 + (n - 1)d \]
where:
- \(a_n\) is the \(n\)-th term of the sequence,
- \(a_1\) is the first term of the sequence,
- \(d\) is the common difference between consecutive terms,
- \(n\) is the term number.
In order to fill in the formula, I need the values for the first term (\(a_1\)) and the common difference (\(d\)). If you can provide these values, I can then complete the explicit formula and calculate the 50th term of the sequence.
For example, if the first term is 3 and the common difference is 2, the explicit formula would be:
\[ a_n = 3 + (n - 1) \cdot 2 \]
Using this to find the 50th term:
\[ a_{50} = 3 + (50 - 1) \cdot 2 \] \[ a_{50} = 3 + 49 \cdot 2 \] \[ a_{50} = 3 + 98 \] \[ a_{50} = 101 \]
Please provide the specific values for \(a_1\) and \(d\) so that I can help you further.
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