Tell whether the sequence is arithmetic. If it is, identify the common difference.
one-half, one-third, one-fourth, ellipsis
(1 point)
Responses
Not arithmetic
Not arithmetic
Arithmetic, common difference is one-sixth
Arithmetic, common difference is Image with alt text: one-sixth
Arithmetic, common difference is two-thirds
Arithmetic, common difference is Image with alt text: two-thirds
Arithmetic, common difference is 1
Not arithmetic
To determine whether the sequence is arithmetic, we need to check if the difference between consecutive terms is constant. Let's examine the given sequence, which consists of the numbers "one-half, one-third, one-fourth, ellipsis."
To find the differences between these terms, we subtract each term from its successive term:
one-third - one-half = -1/6
one-fourth - one-third = -1/12
ellipsis
From this calculation, we see that the differences between the terms are not constant. Therefore, we can conclude that the sequence is not arithmetic.