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

Answer 1

In the given recursively defined arithmetic sequence, we have:

• $a_1=4$
• $a_n=a_{n-1}-5$

In this sequence, the term $a_n$ is defined as the previous term $a_{n-1}$ minus 5. This indicates that each subsequent term is obtained by subtracting 5 from the previous term.

The common difference $d$ of an arithmetic sequence can be identified from the recursive formula. Here, the common difference is:

$$d=-5$$

Thus, the common difference in this arithmetic sequence is $-5$.