Practice Sequence in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An ordered list of numbers generated by a rule, where each number has a specific position (first, second, third, ...).
A pattern of numbers: first term, second term, third term, and so on.
Example 1
easyWrite the first five terms of the sequence a_n = \frac{n}{n+1} for n = 1, 2, 3, \ldots
Example 2
mediumDetermine whether the sequence a_n = \frac{3n^2 + 1}{n^2 + 2} converges or diverges. If it converges, find the limit.
Example 3
easyWrite the first four terms of b_n = (-1)^n \cdot \frac{1}{n}.
Example 4
mediumDetermine whether a_n = \frac{2^n}{n!} converges or diverges.