Question

Is the sequence

6.9,−10,−13.1,−16.2 arithmetic? If so, find the common difference.

a) -3.1
b) -2.3
c) -2.5
d) -3.0

Answer 1

The sequence 6.9, -10, -13.1, -16.2 is an arithmetic sequence with a common difference of -3.1, thus the correct answer is (a) -3.1.

Step-by-step explanation:

To determine whether the sequence 6.9, -10, -13.1, -16.2 is an arithmetic sequence, we can find the differences between consecutive terms:

• The difference between the second term (-10) and the first term (6.9) is -10 - 6.9 = -16.9.
• The difference between the third term (-13.1) and the second term (-10) is -13.1 - (-10) = -3.1.
• The difference between the fourth term (-16.2) and the third term (-13.1) is -16.2 - (-13.1) = -3.1.

The differences between the second and third, and the third and fourth terms are both -3.1, which suggests that this is an arithmetic sequence with a common difference of -3.1. Therefore, the correct answer is (a) -3.1.