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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

5. Geometric Sequences

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Exercise 47 Page 312

Use the formula for the nth term of a geometric sequence, a_n=a_1(r)^(n-1).

59 049

Practice makes perfect

We will start by writing the formula for the nth term of a geometric sequence. We are given that r= 3. a_n= a_1( r)^(n-1) ⇔ a_n= a_1( 3)^(n-1) Let's find a_1 using a_3=81.

a_n=a_1(3)^(n-1)

n= 3, a_()darkviolet3= 81

81=a_1(3)^(3-1)

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Solve for a_1

Subtract term

81=a_1(3)^2

Calculate power

81=a_1(9)

.LHS /9.=.RHS /9.

9=a_1

Rearrange equation

a_1=9

The formula below gives us the nth term of this geometric sequence. a_n= a_1( 3)^(n-1) ⇔ a_n= 9( 3)^(n-1) Now we can find the 9th term.

a_n=9(3)^(n-1)

n= 9

a_()darkviolet9=9(3)^(9-1)

▼

Simplify right-hand side

Subtract term

a_9=9(3)^8

Calculate power

a_9=9(6561)

Multiply

a_9=59 049

The 9th term of the sequence is 59 049.

Subchapter links

Communicate Your Answer p.305

Monitoring Progress p.306-309

Exercises p.310-312