To determine whether the sequence [tex]\(-8.2, -8.4, -8.6, \ldots\)[/tex] is arithmetic or geometric, we should first check the differences between consecutive terms.
### Step-by-Step Solution:
1. Identify the first few terms of the sequence:
- First term ([tex]\(a_1\)[/tex]) = [tex]\(-8.2\)[/tex]
- Second term ([tex]\(a_2\)[/tex]) = [tex]\(-8.4\)[/tex]
- Third term ([tex]\(a_3\)[/tex]) = [tex]\(-8.6\)[/tex]
2. Calculate the differences between consecutive terms (checking for an arithmetic sequence):
- Difference between the second term and the first term:
[tex]\[
a_2 - a_1 = -8.4 - (-8.2) = -8.4 + 8.2 = -0.2
\][/tex]
- Difference between the third term and the second term:
[tex]\[
a_3 - a_2 = -8.6 - (-8.4) = -8.6 + 8.4 = -0.2
\][/tex]
Since the differences between consecutive terms are equal ([tex]\(-0.2\)[/tex]), the sequence is indeed an arithmetic sequence with a common difference.
### Conclusion:
- The common difference [tex]\(d\)[/tex] is [tex]\(-0.2\)[/tex].
The correct answer is:
[tex]\[ d = -0.2 \][/tex]
