Tell whether the sequence is arithmetic. if it is, what is the common difference?

10, 15, 21, 28, …

a.) yes; 5

b.) yes; 6

c.) yes; 7

d.) no

No

Step-by-step explanation:

The sequence is not an arithmetic sequence. For a sequence to be arithmetic, the difference between consecutive terms is a constant number which is termed as the common difference.

This means that the difference between the second term and the first term must be equal to the difference between the third term and the second term.

In the sequence above, the first term is 10. The difference between the first and second term is 15. When the first term is subtracted from the second, what we get is 5.

Now, let’s look at the third term and the second term. The difference here is 21 minus 15 which equals 6. Now we can see that the common difference is not constant and thus we conclude that the series is not arithmetic.