Tell whether the sequence is arithmetic. If it is, identify the common difference. Show your work.
1/2, 1/3, 1/4,...
Not arithmetic
Arithmetic, common difference is 1/6
Arithmetic, common difference is 2/3
Arithmetic, common difference is 1
Not arithmetic
To determine if a sequence is arithmetic, we need to check if there is a common difference between consecutive terms.
In the given sequence, the terms are 1/2, 1/3, 1/4,... Notice that the denominator (the number below the line) of each term is increasing by 1. However, the numerator (the number above the line) is always 1. Therefore, there is no constant difference between consecutive terms, and the sequence is not arithmetic.