Question

In the arithmetic sequence {13,6,−1,−8,…}, what is the common difference? Enter your answer as a number, like this: 42

Answer 1

The common difference of the arithmetic sequence {13, 6, -1, -8, …} is -7, determined by subtracting any term from the subsequent term in the sequence.

Step-by-step explanation:

The common difference in an arithmetic sequence is the constant amount by which consecutive terms differ. To find the common difference, we subtract any term in the sequence from the subsequent term. For instance, in the sequence {13, 6, -1, -8, …}, we subtract the second term (6) from the first term (13) to find the common difference:

13 - 6 = 7

However, because the sequence is decreasing, the common difference is actually negative, which we can also see if we subtract the third term (-1) from the second term (6):

6 - (-1) = 6 + 1 = 7

Thus, the common difference is -7.

Answer 2

-7

Step-by-step explanation:

To find the common difference, you subtract a term from the term after it. For example, in the problem, you can subtract 13 from 6:

6 - 13 = -7

To check you can do the same thing with other consecutive numbers in the sequence like:

-1 - 6 = -7