What is the common difference in the recursively defined arithmetic sequence a1=4

Question

𝑎
1
=
4
, an=an−1−5
◂=▸
.(1 point)
The common difference is .

Answer 1

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

In your case, the sequence is defined as:

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

The common difference \( d \) is the amount that each term differs from the previous term. From the recursive definition \( a_n = a_{n-1} - 5 \), 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 \( -5 \).