To find the common difference of the arithmetic sequence given by the terms [tex]\(-18, -13, -8, \ldots\)[/tex], follow these steps:
1. Identify Consecutive Terms:
- The first term, [tex]\(a_1\)[/tex], is [tex]\(-18\)[/tex].
- The second term, [tex]\(a_2\)[/tex], is [tex]\(-13\)[/tex].
- The third term, [tex]\(a_3\)[/tex], is [tex]\(-8\)[/tex].
2. Calculate the Common Difference:
- Recall that in an arithmetic sequence, the common difference [tex]\(d\)[/tex] is the difference between any two consecutive terms.
3. Find the Difference Between the Second and First Term:
[tex]\[
d = a_2 - a_1
\][/tex]
Substituting the terms, we get:
[tex]\[
d = -13 - (-18)
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
d = -13 + 18
\][/tex]
Now calculate the sum:
[tex]\[
d = 5
\][/tex]
4. Verify the Common Difference with Another Pair of Consecutive Terms:
- Checking the difference between the third term and the second term:
[tex]\[
d = a_3 - a_2
\][/tex]
Substituting the terms, we get:
[tex]\[
d = -8 - (-13)
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
d = -8 + 13
\][/tex]
Now calculate the sum:
[tex]\[
d = 5
\][/tex]
Therefore, the common difference in the arithmetic sequence [tex]\(-18, -13, -8, \ldots\)[/tex] is [tex]\(5\)[/tex].
