Question

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

Answer 1

In the recursively defined arithmetic sequence given by:

- \( a_1 = 4 \)
- \( a_n = a_{n-1} - 5 \)

The common difference \( d \) can be identified as the amount you subtract to get from one term to the next.

From the definition, each term is formed by subtracting 5 from the previous term. This means that the common difference is:

\[
d = -5
\]

Thus, the common difference in this arithmetic sequence is \( -5 \).