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Sequences and series
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.
Sal explains what sequences are and gives examples of different sequences, defined either explicitly or recursively, and discusses different notations for sequences.
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.
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?
Sal solves the following problem: What is the value of the 100th term in the sequence 15, 9, 3, -3...
Equations of Sequence Patterns
Given an arithmetic sequence, ether in explicit form or in recursive form, find a specific term in the sequence.
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 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.
Find the sum of the first n terms of an arithmetic sequence.