Question

Question
What is the common difference in the recursively defined arithmetic sequence a1=4
, an=an−1−5
.(1 point)
The common difference is
.
Remaining Attempts : 3

Answer 1

In a recursively defined arithmetic sequence, the common difference can be found from the recursive formula.

Here, the sequence is defined as:
- \( a_1 = 4 \)
- \( a_n = a_{n-1} - 5 \)

The common difference \( d \) is the value that is added (or subtracted in this case) to get from one term to the next. In this case, we see that \( a_n \) is formed by subtracting 5 from the previous term \( a_{n-1} \).

Thus, the common difference is:
\[ d = -5 \]

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