Final answer:
The recursive rule (a₁ = 2), (aₙ = 7aₙ₋₁) represents a geometric sequence because each term is obtained by multiplying the previous term by the constant ratio of 7.
Step-by-step explanation:
To determine whether the recursive rule (a₁ = 2), (aₙ = 7aₙ₋₁) represents an arithmetic sequence or a geometric sequence, we must analyze the relationship between consecutive terms. In an arithmetic sequence, each term is obtained by adding a constant to the previous term, while in a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio.
In the given recursive rule, each term aₙ is found by multiplying the previous term aₙ₋₁ by 7. This means that every term is 7 times the term before it. Therefore, the sequence is geometric, not arithmetic, because it involves multiplying by a constant ratio to obtain the consecutive terms.
It follows the formula (aₙ = a₁ × r^(n-1)) where a₁ is the first term, r is the common ratio, and n is the term number. Applying this to the rule given, with a₁ = 2 and r = 7, confirms that this is indeed a geometric sequence.