Arithmetic Sequences: Crack the Formula to Predict Any Term [Intro]
Imagine you are building a staircase out of wooden blocks. The first step takes 3 blocks. The second takes 5. The third takes 7, and the fourth takes 9. If you want to build a massive staircase with 100 steps, do you really want to sit there adding 2 over and over again? Of course not. This predictable, stepping-stone pattern is what mathematicians call an Arithmetic Sequence. Today, we are going to crack the code behind these linear patterns so you can predict the value of any step in an infinite chain instantly, without doing the manual grunt work.
You’ll learn:
The essential vocabulary of sequences: Sequence, Arithmetic, and Common Difference.
The logic behind the Arithmetic Sequence Formula.
How to identify the first term and the common difference from a given pattern.
How to find the value of any term, like the 25th term, without listing all the previous terms.
How to work backward: finding the common difference when given the first term and a later term.
How to find the total number of terms in a sequence when given the first and last terms.
This lesson is ideal for students in Grade 10–12 math courses including Pre-Calculus, Algebra II, Functions, or Advanced Functions, as well as those studying AP Precalculus, AP Calculus, IB Mathematics (AA SL/HL), IGCSE, or A-Level Math. This can also help those enrolled in post-secondary Calculus courses.
Chapters
00:00 - Introduction
00:06 - What is an Arithmetic Sequence?
3:39 - Examples with Arithmetic Sequences.
8:36 - Recap and Check Your Understanding Question
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