# Sequences and series

1 article

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...

### 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.

### Series as sum of sequence

VIDEO
2:53 minutes