Next in Sequence: Find Any Term in an Arithmetic Series [Intro]
In our last video, we looked at arithmetic sequences, lists of numbers that grow by a constant step. But what happens if you don't just want to list those numbers, you want to add them all up? Imagine you get a new job where you make $100 on your first day, $105 on your second day, $110 on your third, and so on. If you want to calculate exactly how much money you’ve banked after a full year, listing 365 terms is a nightmare. This is an Arithmetic Series: the sum of an arithmetic sequence. Today, we are going to use the genius trick discovered by a 10-year-old schoolboy named Carl Friedrich Gauss to find the sum of any linear progression instantly.
Relevant Videos:
Arithmetic Sequences [Intro] - • Arithmetic Sequences: Crack the Formula to...
You’ll learn:
The story of Gauss's brilliant trick for adding numbers from 1 to 100 and the logic behind it.
The two essential Arithmetic Series Formulas: one using the first and last terms, and one using the common difference.
How to find the sum of the first 40 terms of a series like 3+7+11+15+…
How to work backward to find the number of terms in a series when given the sum and the first/last terms.
How to solve for the first term when given the number of terms, the common difference, and the total sum.
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 - The Arithmetic Series Formulae
3:16 - Example of Using the Sn Formula Without Last Term Given
4:49 - Example of Using the Sn Formula With Last Term Given
6:07 - Example of Working Backwards
7:45 - Recap and Check Your Understanding
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