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

Question

The common difference is _______.

Answer 1

In an arithmetic sequence, the common difference is the value that is added to each term to get the next term.

In the recursively defined arithmetic sequence you've provided, \( a_1 = 4 \) and \( a_n = a_{n-1} - 5 \), we can see how the sequence progresses:

• \( a_1 = 4 \)
• \( a_2 = a_1 - 5 = 4 - 5 = -1 \)
• \( a_3 = a_2 - 5 = -1 - 5 = -6 \)
• \( a_4 = a_3 - 5 = -6 - 5 = -11 \)

From this, we see that each term is obtained by subtracting 5 from the previous term.

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

So, the common difference is -5.