Question

Determine if the given sequence is an arithmetic sequence. If it​ is, find the common​ difference, d.
Start 2 By 5 Table 1st Row 1st Column n 2nd Column 1 3rd Column 2 4st Column 3 5st Column 4 2nd Row 1st Column f left parenthesis n right parenthesis 2nd Column negative 10 3rd Column negative 16 4st Column negative 22 5st Column negative 28 EndTable

Question content area bottom
Part 1
Is this an arithmetic​ sequence?
No
Yes

Answer 1

To determine if the given sequence is an arithmetic sequence, we need to check if the differences between consecutive terms are constant.

The sequence provided in the table is:
- \( f(1) = -10 \)
- \( f(2) = -16 \)
- \( f(3) = -22 \)
- \( f(4) = -28 \)

Now, let's find the differences between consecutive terms:

1. \( f(2) - f(1) = -16 - (-10) = -16 + 10 = -6 \)
2. \( f(3) - f(2) = -22 - (-16) = -22 + 16 = -6 \)
3. \( f(4) - f(3) = -28 - (-22) = -28 + 22 = -6 \)

Since the difference between consecutive terms is constant (all differences equal -6), this sequence is indeed an arithmetic sequence.

Therefore, the answer is:
**Yes**, it is an arithmetic sequence, and the common difference \( d = -6 \).