Is the sequence left-brace a subscript n baseline right-brace equals left-brace 13 comma 20 comma 27 comma 34 comma ellipsis right-brace arithmetic? If so, identify the common difference.

Question

(1 point)
Responses

yes, 7
yes, 7

yes,negative 7
yes, Image with alt text: negative 7

yes, 13
yes, 13

no
no

Answer 1

To determine whether the sequence \({a_n} = {13, 20, 27, 34, \ldots}\) is arithmetic, we need to check if the differences between consecutive terms are constant.

The sequence can be examined as follows:

• The difference between the second term (20) and the first term (13) is: \[ 20 - 13 = 7 \]
• The difference between the third term (27) and the second term (20) is: \[ 27 - 20 = 7 \]
• The difference between the fourth term (34) and the third term (27) is: \[ 34 - 27 = 7 \]

Since the difference between consecutive terms is constant and equal to 7, we can conclude that the sequence is indeed arithmetic, and the common difference is 7.

Therefore, the correct response is: yes, 7.