Arithmetic SEQUENCES & Arithmetic SERIES - Introduction

Hello! In this video, I will talk about arithmetic sequences and arithmetic series. First, I explain what an arithmetic sequence is. A sequence is a list of numbers with commas separating each term. There may or may not be a pattern between each term. A sequence does not need to begin with number 1. Just because the first term is 1, it does not mean that the second term cannot be 1 too.

An arithmetic sequence is a sequence of numbers that have a common difference. This means the difference between the first and second, second and third, third and fourth term and so on are the same. This is what we call a common difference. If the sequence has a common difference, then it is considered an arithmetic sequence. Please note that there are other types of sequences, not just arithmetic. There is such thing called a geometric sequence and a sequence that does not follow any rules (not arithmetic or geometric).

Common questions asked are what is the nth term, given the first few terms. Another question, they will give you two random non-consecutive term and ask for the common difference.

Formulas mentioned in this video:
a_n = a_1+ (n-1)d
d = [(a_y) - (a_x)] / (y-x)
a_1 + a_2 + ... + a_n = (n/2)(a_1 + a_n)

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