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Pearson Algebra 2 Common Core, 2011 View details

Cumulative Standards Review

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Exercise 1 Page 898

Use the formula for the sum of a finite geometric series.

Practice makes perfect

To evaluate the sum of the finite geometric series, we need to know the first term, the common ratio, and the number of terms of the related geometric sequence.

We can see that the common ratio is 2 and the first term is 2. Let's write the explicit formula of the related sequence!

a_n=a_1 r^(n-1)

SubstituteII

r= 2, a_1= 2

a_n= 2 * 2^(n-1)

Now, to calculate the number of terms, we will find what value of n corresponds to the last term, 64. To do so, we will substitute 64 for a_n in our formula, and solve for n.

a_n=2 * 2^(n-1)

Substitute

a_n= 64

64=2 * 2^(n-1)

▼

Solve for n

DivEqn

.LHS /2.=.RHS /2.

32=2^(n-1)

WritePow

Write as a power

2^5=2^(n-1)

EquateExponents

Equate exponents

5=n-1

AddEqn

LHS+1=RHS+1

6=n

RearrangeEqn

Rearrange equation

n=6

There are 6 terms. Finally, to evaluate the given series, we will substitute r=2, a_1=2, and n=6 into the formula for the sum of a finite geometric series.

S_n=a_1(1-r^n)/1-r

SubstituteValues

Substitute values

S_6=2(1- 2^6)/1- 2

▼

Evaluate right-hand side

CalcPow

Calculate power

S_6=2(1-64)/1- 2

SubTerms

Subtract terms

S_6=2(- 63)/- 1