Final answer:
The sequence given by An = -13 + 7(n-4) is an arithmetic sequence, as it can be simplified to An = 7n - 41, which shows a common difference (d) of 7 between successive terms.
Step-by-step explanation:
The student has asked whether the sequence with the nth term given by An = -13 + 7 (n-4) is an arithmetic sequence. An arithmetic sequence is defined by the presence of a common difference between successive terms. To determine if this sequence is arithmetic, we can simplify the expression for the nth term and examine it.
The nth term can be rewritten as:
- An = -13 + 7n - 28
- An = 7n - 41
This is now in the form An = dn + c where d is the common difference and c is a constant. It’s clear that the common difference, d, is 7 because each term increases by 7 as n increases by 1. Therefore, the sequence is indeed an arithmetic sequence.