![]() Connections are made between arithmetic sequences and equations of lines and the explicit formula for an arithmetic sequence is given as an d(n)+a0 a n d ( n) + a 0. Sigma Notation is introduced, as well as Arithmetic and Geometric Sequences. Faculty Member at Technological Institute of the Philippines (T.I.P. ![]() These formulas are introduced in the lesson Arithmetic progressions under the current topic in this site. Chapter 8 gives a brief introduction to sequences and series. , is the geometric progression with the first term and the common ratio then the formula for the sum of its first n terms is. Formula for sum of a geometric progression. These are the formula for the n-th term of an arithmetic progression and the formula for the sum of the first n terms of an arithmetic progression. By applying the last formula again and again you have the chain of equalities. In the context of an explicit formula like '-5+2(n-1)' 'n-1' represents how many times we need to add 2 to the first term to get the n-th term. In this lesson you will learn the proofs of the formulas for arithmetic progressions. In the context of a recursive formula where we have 'n-1' in subindex of 'a', you can think of 'a' as the previous term in the sequence. ![]() The proofs of the formulas for arithmetic progressions Source code of 'The proofs of the formulas for arithmetic progressions' This Lesson (The proofs of the formulas for arithmetic progressions) was created by by ikleyn(48724) : View Source, Show
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