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 \(-5\).