The explicit formula given is:
\[ a_n = 8 + 7(n - 1) \]
a) The formula is finding the \( n \)-th term of the sequence, so we can denote that \( a_n \) represents the \( n \)-th term of the sequence.
b) To find the specific term represented by \( a_5 \), we need to replace \( n \) with 5 in the formula.
Thus, we should replace \( n \) with 5:
\[ a_5 = 8 + 7(5 - 1) \]
Calculating this:
\[ a_5 = 8 + 7(4) = 8 + 28 = 36 \]
However, you asked for what value should replace \( n \) to identify the correct term. Looking solely at the definition of \( a_5 \), the value of \( n \) that corresponds to this term is 5.
Therefore:
- a) The formula is finding the \( n \)-th term of the sequence.
- b) The value that should replace \( n \) is 5.
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