What is the common difference in the recursively defined arithmetic sequence a1=4, an=an−1−5.

Answer 1

To find the common difference in a recursively defined arithmetic sequence, we need to find the difference between consecutive terms. We are given that a(n) = a(n-1) - 5.

So, we can find the difference between a(n) and a(n-1) as follows:
a(n) - a(n-1) = (a(n-1) - 5) - a(n-1)
= -5

Therefore, the common difference in this recursively defined arithmetic sequence is -5.