Find the recursive formula for the arithmetic sequence 7, 5, 3, 1, -1, . . . .
A. a1 = 7, a n = a n-1 - 2
B. a1 = 7, a n = 2a n-1
C. a1 = 7, a n =-2 a n-1
D. a1 = 7, a n = a n-1 + 2
The recursive formula for an arithmetic sequence is given by the formula:
a_n = a_(n-1) + d,
where a_n is the nth term in the sequence, a_(n-1) is the previous term, and d is the common difference between consecutive terms.
In this case, the common difference between consecutive terms is -2. Therefore, the recursive formula for the arithmetic sequence 7, 5, 3, 1, -1, . . . is:
a_n = a_(n-1) - 2.
So, the correct answer is A. a1 = 7, a_n = a_(n-1) - 2.