Question

Find the recursive formula for the arithmetic sequence 7, 5, 3, 1, −1, . . .

Answer 1

Common difference = 5−7 = −2, so subtract 2 each step.

Recursive formula (starting at n=1):
a1 = 7
a_n = a_{n-1} − 2 for n ≥ 2

(Explicit: a_n = 7 + (n−1)(-2) = 9 − 2n.)