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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12.3 Geometric Sequences

Focus on geometric nth term and finite geometric sum.

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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.

01nth term of a geometric sequenceWorked steps · five questions02Partial sums of geometric sequencesWorked steps · five questions03Infinite geometric seriesWorked steps · five questions
Lesson brief and rules

12.3 Geometric Sequences

an=a1rn−1a_{n}=a_{1}r^{n-1}, where rr is the common ratio.

Worked example 11
01 / A geometric sequence has a1=3a_{1}=3 and r=2r=2. Find a22.
02 / an=a1rn−1=3⋅21=6a_{n}=a_{1}r^{n-1}=3\cdot 2^{1}=6.
03 / Answer: 66
Worked example 2 · Finite geometric sum

Find the sum 4+8+164+8+16.

Add a(1+2+4)=7a=28a(1+2+4)=7a=28. Answer: 2828

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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