Sure! Let's find the common difference of the arithmetic sequence [tex]\(-4, -12, -20, \ldots\)[/tex].
An arithmetic sequence is a sequence of numbers in which the difference of any two successive members is a constant, called the common difference.
Here's the step-by-step process:
1. Identify the first term of the sequence.
- The first term, [tex]\(a_1\)[/tex], is [tex]\(-4\)[/tex].
2. Identify the second term of the sequence.
- The second term, [tex]\(a_2\)[/tex], is [tex]\(-12\)[/tex].
3. To find the common difference ([tex]\(d\)[/tex]), subtract the first term from the second term.
[tex]\[
d = a_2 - a_1
\][/tex]
4. Substitute the values of [tex]\(a_2\)[/tex] and [tex]\(a_1\)[/tex]:
[tex]\[
d = -12 - (-4)
\][/tex]
5. Simplify the expression:
[tex]\[
d = -12 + 4
\][/tex]
6. Complete the calculation:
[tex]\[
d = -8
\][/tex]
So, the common difference of the given arithmetic sequence [tex]\(-4, -12, -20, \ldots\)[/tex] is [tex]\(-8\)[/tex].
[tex]\[
\boxed{-8}
\][/tex]
