Arithmetic sequences and the sum of the terms of an arithmetic sequence
I'll introduce you to arithmetic sequences with a concrete example of an application where you naturally need to know the sum of the terms in an arithmetic sequence. I'll explain the formula and show you how to find it visually. We'll first look at the case of the sum of consecutive integers, then generalize it to the case of any arithmetic sequence.
#maths
00:00 Arithmetic Sequences
Introductory example and definition, concept of the common difference of an arithmetic sequence
01:01 Sum of Consecutive Integers
Formula for calculating the sum 1 + 2 + ... + n
01:50 Generalization to Any Sequences
The most general formula for the sum of consecutive terms in an arithmetic sequence, valid regardless of the first term and the common difference of the sequence.