MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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12.1 Sequences and Summation Notation

Focus on summation and sequence term.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Terms of a sequenceWorked steps · five questions02Recursive sequencesWorked steps · five questions03Partial sums and sigma notationWorked steps · five questions
Lesson brief and rules

12.1 Sequences and Summation Notation

The notation ∑\sum from k=1k=1 to nn adds the terms for each integer kk.

Worked example 11
01 / Evaluate ∑\sum from j=1j=1 to 22 of 33.
02 / There are 22 terms each equal to 33; sum =6=6.
03 / Answer: 66
Worked example 2 · Sequence term

If an=4na_{n}=4n, find a66.

Substitute n=6n=6: a6=24a6=24. Answer: 2424

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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