Sequences and series

5 videos
5 skills
This sequence (pun intended) of videos and exercises will help us explore ordered lists of objects--even infinite ones--that often have some pattern to them. We will then explore constructing sequences where the nth term is the sum of the first n terms of another sequence (series). This is surprisingly useful in a whole series (pun intended) of applications from finance to drug dosage.

Introduction to sequences

VIDEO 8:18 minutes
Sal explains what sequences are and gives examples of different sequences, defined either explicitly or recursively, and discusses different notations for sequences.

Introduction to arithmetic sequences

VIDEO 7:07 minutes
Sal introduces arithmetic sequences and their main features, the initial term and the common difference. He gives various examples of such sequences, defined explicitly and recursively.

Find the next term of an arithmetic sequence, given the first few terms

PRACTICE PROBLEMS
Solve problems such as: The first four terms of an arithmetic sequence are -5, -1, 3, and 7. What is the fifth term in the sequence?

How to find the 100th term of a sequence given the first four terms (example)

VIDEO 5:57 minutes
Sal solves the following problem: What is the value of the 100th term in the sequence 15, 9, 3, -3...

Equations of sequence patterns

VIDEO 8:36 minutes
Equations of Sequence Patterns

Find any term of an arithmetic sequence, given the formula of the sequence

PRACTICE PROBLEMS
Given an arithmetic sequence, ether in explicit form or in recursive form, find a specific term in the sequence.

Find explicit formulas for arithmetic sequences

PRACTICE PROBLEMS
Solve problems such as: The first four terms in an arithmetic sequence are 12, 5, -2, and -9. Find an explicit formula for the sequence.

Find recursive formulas for arithmetic sequences

PRACTICE PROBLEMS
Find the recursive formula of an arithmetic sequence given the first few terms or given an explicit formula. Convert a recursive formula to an explicit formula.

Arithmetic series

PRACTICE PROBLEMS
Find the sum of the first n terms of an arithmetic sequence.