Find the common difference or common ratio of the sequence \( -8.2,-8.4,-8.6, \ldots \) ? a. \( r=0.2 \) b. \( r=-0.2 \) c. \( d=0.2 \) d. \( d=-0.2 \)

The given sequence is \( -8.2, -8.4, -8.6, \ldots \). To determine whether it's an arithmetic or geometric sequence, let's examine the differences and ratios between consecutive terms: 1. **Arithmetic Sequence (Common Difference \( d \)):** - Calculate the difference between consecutive terms: \[ -8.4 - (-8.2) = -0.2 \] \[ -8.6 - (-8.4) = -0.2 \] - Since the difference is constant (\( -0.2 \)), the sequence is arithmetic with a common difference: \[ d = -0.2 \] 2. **Geometric Sequence (Common Ratio \( r \)):** - Calculate the ratio between consecutive terms: \[ \frac{-8.4}{-8.2} \approx 1.024 \] \[ \frac{-8.6}{-8.4} \approx 1.024 \] - Although the ratios appear roughly consistent, the sequence is more straightforwardly identified as arithmetic due to the clear constant difference. Given the options, the correct choice is: **d. \( d = -0.2 \)**