Answer: a(n) = a(n-1) - 7, with a(1) = -31.
Explanation:
In a recursive sequence, each term is defined by the previous term(s) and some fixed formula or rule. In this case, the formula is given as a(n) = -31 - 7(n-1), which means that each term is obtained by subtracting 7 from the previous term, starting with a(1) = -31. This can be expressed recursively as:
a(n) = a(n-1) - 7
with the initial condition a(1) = -31. This formula says that to get the nth term, we subtract 7 from the (n-1)th term. So, for example:
a(2) = a(1) - 7 = -31 - 7 = -38
a(3) = a(2) - 7 = -38 - 7 = -45
a(4) = a(3) - 7 = -45 - 7 = -52
and so on.