Classify the sequence left brace lower a subscript lower n baseline right brace equals left brace 1 comma 16 comma 31 comma 46 comma ellipsis right brace as arithmetic, geometric, or neither. If there is not enough information to classify the sequence, choose not enough information.

Question

(1 point)
Responses

arithmetic
arithmetic

geometric
geometric

neither
neither

not enough information

Answer 1

To classify the sequence \( {a_n} = {1, 16, 31, 46, \ldots} \), we need to determine the pattern of the terms.

Let's look at the differences between consecutive terms:

• The difference between the 1st term (1) and the 2nd term (16) is \( 16 - 1 = 15 \).
• The difference between the 2nd term (16) and the 3rd term (31) is \( 31 - 16 = 15 \).
• The difference between the 3rd term (31) and the 4th term (46) is \( 46 - 31 = 15 \).

Since the difference between consecutive terms is constant (15), the sequence is classified as arithmetic.

Therefore, the correct response is:

arithmetic