1. The problem asks to identify which statement does NOT describe the explicit arithmetic formula.
2. The explicit arithmetic formula for an arithmetic sequence is given by:
$$a_n = a_1 + (n-1)d$$
where $a_n$ is the $n$th term, $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number.
3. Important rules:
- The formula uses the first term $a_1$ and the common difference $d$.
- It can find any term directly without needing previous terms.
4. Evaluate each statement:
- "The explicit arithmetic formula adds the common difference to the previous term." This describes the recursive formula, not the explicit formula.
- "The explicit arithmetic formula can easily find a term far into a sequence." This is true.
- "The explicit arithmetic formula has a common difference." This is true.
- "In the explicit arithmetic formula, $a_1$ represents the first term in the sequence." This is true.
5. Therefore, the statement that does NOT describe the explicit arithmetic formula is:
"The explicit arithmetic formula adds the common difference to the previous term."
Explicit Arithmetic E58E08
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