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Big Ideas Math Algebra 1, 2015

BI

Big Ideas Math Algebra 1, 2015 View details

6. Geometric Sequences

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Exercise 30 Page 336

To find the explicit formula, calculate the common ratio first.

Equation: a_n=-192 ( -1/4 )^(n-1)
Value of a_6: 3/16

Practice makes perfect

We want to find the equation for the nth term and the value of the sixth term of the given geometric sequence. First we will find its explicit formula. Let's start by calculating the common ratio using the four terms given in the table, -192, 48, -12, and 3.

We will now use the common ratio - 14 and the first term -192 to write the formula. a_n=a_1r^(n-1) ⇔ a_n= -192( - 1/4 )^(n-1) Finally, to calculate the value of a_6 we will substitute 6 for n in our formula.

a_n=-192(-1/4)^(n-1)

n= 6

a_6=-192( - 1/4 )^(6-1)

▼

Evaluate right-hand side

Subtract term

a_6=-192( - 1/4 )^5

MoveNegFracToDenom

Put minus sign in denominator

a_6=-192( 1/-4 )^5

(a/b)^m=a^m/b^m

a_6=-192 ( 1/-1024)

MoveLeftFacToNumOne

a* 1/b= a/b

a_6=-192/-1024

- a/- b=a/b

a_6=192/1024

a/b=.a /64./.b /64.

a_6 = 3/16

Subchapter links

Communicate Your Answer p.331

Monitoring Progress p.332-335