To find the common difference of the given arithmetic sequence [tex]\(5, 0, -5, \ldots\)[/tex]:
1. Identify the first term (a1):
The first term of the sequence is given as [tex]\(a_1 = 5\)[/tex].
2. Identify the second term (a2):
The second term of the sequence is given as [tex]\(a_2 = 0\)[/tex].
3. Calculate the common difference (d):
The common difference in an arithmetic sequence is the amount added to each term to get to the next term. It is calculated as the difference between the second term and the first term. Specifically, the common difference [tex]\(d\)[/tex] is:
[tex]\[
d = a_2 - a_1
\][/tex]
4. Substitute the known values:
[tex]\[
d = 0 - 5 = -5
\][/tex]
Thus, the common difference of the arithmetic sequence [tex]\(5, 0, -5, \ldots\)[/tex] is [tex]\(-5\)[/tex].
