Question

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

Answer 1

The common difference in a recursively defined arithmetic sequence can be found by subtracting each term from the next term.

In this case, the formula for finding the n-th term is given by:
an = an-1 - 5

To find the common difference, we can start with finding the second term (a2):
a2 = a1 - 5
= 4 - 5
= -1

Now, we can find the common difference by subtracting a2 from a1:
Common difference = a2 - a1
= (-1) - 4
= -5

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