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

easy
Write the first five terms of the sequence a_n = \frac{n}{n+1} for n = 1, 2, 3, \ldots

Example 2

medium
Determine whether the sequence a_n = \frac{3n^2 + 1}{n^2 + 2} converges or diverges. If it converges, find the limit.

Example 3

easy
Write the first four terms of b_n = (-1)^n \cdot \frac{1}{n}.

Example 4

medium
Determine whether a_n = \frac{2^n}{n!} converges or diverges.