To find the common difference of the arithmetic sequence [tex]\(-17, -15, -13, \ldots\)[/tex], follow these steps:
1. Identify the first two terms of the sequence:
The first term ([tex]\(a_1\)[/tex]) is [tex]\(-17\)[/tex].
The second term ([tex]\(a_2\)[/tex]) is [tex]\(-15\)[/tex].
2. Recall the formula for the common difference in an arithmetic sequence:
The common difference ([tex]\(d\)[/tex]) can be found using the difference between any two consecutive terms. Specifically:
[tex]\[
d = a_{n+1} - a_n
\][/tex]
where [tex]\(a_{n+1}\)[/tex] is the term following [tex]\(a_n\)[/tex].
3. Substitute the values of the first two terms into the formula:
[tex]\[
d = a_2 - a_1 = -15 - (-17)
\][/tex]
4. Simplify the expression inside the parentheses:
[tex]\[
d = -15 + 17
\][/tex]
5. Calculate the result:
[tex]\[
d = 2
\][/tex]
Thus, the common difference of the arithmetic sequence [tex]\(-17, -15, -13, \ldots\)[/tex] is [tex]\(2\)[/tex].
