Find the common difference of this arithmetic sequence: a_(n) = -8n +14

since -8(n+1) - (-8n) = -8

the common difference is -8

To find the common difference of an arithmetic sequence, we need to find the difference between consecutive terms.

In the given arithmetic sequence, the general form of the nth term is given by a(n) = -8n + 14.

Let's find the difference between two consecutive terms:

a(n+1) - a(n) = [-8(n+1) + 14] - [-8n + 14]
= -8n - 8 + 14 + 8n - 14
= -8n + 8n
= 0

Since the difference between consecutive terms is 0, it means that all the terms in the sequence are the same. Therefore, this sequence has a common difference of 0.

To find the common difference of an arithmetic sequence, you need to examine the equation that represents the sequence. In this case, the arithmetic sequence is represented by the equation:

a_n = -8n + 14

In an arithmetic sequence, each term is obtained by adding a constant difference (d) to the previous term. The common difference represents this constant difference.

Comparing the given equation to the general form of an arithmetic sequence, a_n = a_1 + (n-1)d, we can see that the first term (a_1) is 14, and the constant difference (d) is -8.

Therefore, the common difference of this arithmetic sequence is -8.