9.3 Geometric Sequences

A geometric sequence is a sequence in which each term after the first term "a" is obtained by multiplying the previous term by a constant r, called the common ratio.












Finding an Explicit Term

Example 1: 5, 15, 45, 135,... Find the 8th term

Find the common ratio

r=3
Plug into equation a_n= (a₁)(r^n-1)

a₈= (5)(3^8-1)

a₈= (5)(3⁷)

a₈= 54,675

Finding the sum of a Geometric Sequence

Equation for the sum: S_n= a₁[(1-rⁿ)/1-r]

Example 2: Evaluate S₁₀ for 250, 100, 40, 16,... 

Find Common Ratio

100/250= 2/5 40/100= 2/5 16/40= 2/5

r=2/5

Plug into equation S_n= a₁[(1-rⁿ)/1-r]

S₁₀= 250[(1–(2/5)¹⁰)/1–(2/5)

S₁₀= 6509734/15625

If you still don't get it check out these videos

A Quick Intro to Geometric Sequences

Geometric Sequences (Introduction)