Question

What is the common difference in the recursively defined arithmetic sequence a1=4
, an=an−1−5
.(1 point)
The common difference is
a
.

Answer 1

In the recursively defined arithmetic sequence you provided, the first term is \( a_1 = 4 \) and the recursively defined formula is \( a_n = a_{n-1} - 5 \).

The common difference \( d \) in an arithmetic sequence is the constant amount that each term differs from the previous term.

From the recursive formula \( a_n = a_{n-1} - 5 \), we can see that each term is obtained by subtracting 5 from the previous term. Therefore, the common difference is:

\[
d = -5
\]

So, the common difference is \(-5\).