Question 1

Find the sum of the finite geometric sequence.(Round your answer to three decimal places. )? $$\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }$$ ?

Accepted Answer

A) 2,092.596 
B) 1,691.128 
C) 340.518 
D) 352.212 
E) 1,312.385 
A) 2,092.596 
B) 1,691.128 
C) 340.518 
D) 352.212 
E) 1,312.385

Question 2

Find the sum of the finite geometric sequence? $$\sum _ { n = 1 } ^ { 6 } ( - 6 ) ^ { n - 1 }$$ ?

Accepted Answer

A) -6,665 
B) -9,331 
C) -185 
D) 1,555 
E) 1,111 
A) -6,665 
B) -9,331 
C) -185 
D) 1,555 
E) 1,111

Question 3

Write the nth term of the geometric sequence as a function of n. $$a _ { 1 } = 2 , a _ { k + 1 } = 4 a _ { k }$$

Accepted Answer

A)  $a _ { n } = 2 ( 4 ) ^ { n - 1 }$ 
B)  $a _ { n } = - 2 + 4 n$ 
C)  $a _ { n } = 2 ( 4 ) ^ { n }$ 
D)  $a _ { n } = 2 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
E)  $a _ { n } = 4 ( 2 ) ^ { n - 1 }$ 
A)  $a _ { n } = 2 ( 4 ) ^ { n - 1 }$ 
B)  $a _ { n } = - 2 + 4 n$ 
C)  $a _ { n } = 2 ( 4 ) ^ { n }$ 
D)  $a _ { n } = 2 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
E)  $a _ { n } = 4 ( 2 ) ^ { n - 1 }$

Question 4

Use a graphing utility to graph the first 10 terms of the sequence.? $$a _ { n } = 3 ( - 0.7 ) ^ { n - 1 }$$

Accepted Answer

A) ? ?   
B) ? ?   
C) ?   ? 
D) ? ?   
E)    
A) ? ?   
B) ? ?   
C) ?   ? 
D) ? ?   
E)

Question 5

Find the indicated nth term of the geometric sequence. ?
22th term : $$8,32,128 , \ldots$$ ?

Accepted Answer

A)  $a _ { 22 } = 35,184,372,088,832$ 
B)  $a _ { 22 } = 549,755,813,888$ 
C)  $a _ { 22 } = 2,199,023,255,552$ 
D)  $a _ { 22 } = 8,796,093,022,208$ 
E)  $a _ { 22 } = 140,737,488,355,328$ 
A)  $a _ { 22 } = 35,184,372,088,832$ 
B)  $a _ { 22 } = 549,755,813,888$ 
C)  $a _ { 22 } = 2,199,023,255,552$ 
D)  $a _ { 22 } = 8,796,093,022,208$ 
E)  $a _ { 22 } = 140,737,488,355,328$

Question 6

Find the sum of the infinite geometric series.? $$\sum _ { n = 0 } ^ { \infty } \left( - \frac { 1 } { 8 } \right) ^ { n }$$ ?

Accepted Answer

A)  $\frac { 8 } { 9 }$ 
B)  $- \frac { 8 } { 9 }$ 
C)  $- \frac { 9 } { 8 }$ 
D)  $\frac { 9 } { 10 }$ 
E)  $\frac { 9 } { 8 }$ 
A)  $\frac { 8 } { 9 }$ 
B)  $- \frac { 8 } { 9 }$ 
C)  $- \frac { 9 } { 8 }$ 
D)  $\frac { 9 } { 10 }$ 
E)  $\frac { 9 } { 8 }$

Question 7

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places. )? $$a _ { 1 } = 7 , r = \sqrt { 3 } , n = 8$$ ?

Accepted Answer

A)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n - 1 }$ ,About 15.456 
B)  $a _ { n } = ( \sqrt { 3 } ) ^ { n - 1 }$ ,About 982.073 
C)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n + 1 }$ ,About 327.358 
D)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n - 1 }$ ,About 327.358 
E)  $a _ { n } = ( \sqrt { 3 } ) ^ { n + 1 }$ ,About 15.456 
A)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n - 1 }$ ,About 15.456 
B)  $a _ { n } = ( \sqrt { 3 } ) ^ { n - 1 }$ ,About 982.073 
C)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n + 1 }$ ,About 327.358 
D)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n - 1 }$ ,About 327.358 
E)  $a _ { n } = ( \sqrt { 3 } ) ^ { n + 1 }$ ,About 15.456

Question 8

Find the first five terms of the geometric sequence.? $$a _ { 1 } = 4 , r = \pi$$ ?

Accepted Answer

A)  $$4,4 \pi , 4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 }$$ 
B)  $4,4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 } , 4 \pi ^ { 5 }$ 
C)  $4 , \pi ^ { 2 } , \pi ^ { 3 } , \pi ^ { 4 } , \pi ^ { 5 }$ 
D)  $4 , \pi , \pi ^ { 2 } , \pi ^ { 3 } , \pi ^ { 4 }$ 
E)  $4 , \pi , 4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 }$ 
A)  $$4,4 \pi , 4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 }$$ 
B)  $4,4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 } , 4 \pi ^ { 5 }$ 
C)  $4 , \pi ^ { 2 } , \pi ^ { 3 } , \pi ^ { 4 } , \pi ^ { 5 }$ 
D)  $4 , \pi , \pi ^ { 2 } , \pi ^ { 3 } , \pi ^ { 4 }$ 
E)  $4 , \pi , 4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 }$

Question 9

Find the first five terms of the geometric sequence.? $$a _ { 1 } = 5 , r = 3$$ ?

Accepted Answer

A)  $$5,15,45,135,405$$ 
B)  $$9,27,81,243,729$$ 
C)  $15,45,135,405,1215$ 
D)  $1,3,9,27,81$ 
E)  $3,9,27,81,243$ 
A)  $$5,15,45,135,405$$ 
B)  $$9,27,81,243,729$$ 
C)  $15,45,135,405,1215$ 
D)  $1,3,9,27,81$ 
E)  $3,9,27,81,243$

Question 10

?Find the sum of the finite geometric sequence. ?? $$\sum _ { n = 1 } ^ { 10 } \left( - \frac { 3 } { 4 } \right) ^ { n - 1 }$$ ?

Accepted Answer

A) ? $\frac { 1,225,723 } { 262,144 }$ 
B) ? $\frac { 141,361 } { 262,144 }$ 
C) ? $\frac { 1,068,259 } { 262,144 }$ 
D) ? $- \frac { 1,225,723 } { 262,144 }$ 
E) ? $- \frac { 1,068,259 } { 262,144 }$ 
A) ? $\frac { 1,225,723 } { 262,144 }$ 
B) ? $\frac { 141,361 } { 262,144 }$ 
C) ? $\frac { 1,068,259 } { 262,144 }$ 
D) ? $- \frac { 1,225,723 } { 262,144 }$ 
E) ? $- \frac { 1,068,259 } { 262,144 }$

Question 11

Determine whether the sequence is geometric.If so,find the common ratio. -2,2,6,10,...

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B) -2 
C) 4 
D) not geometric 
E) -4 
A)  $\frac { 1 } { 4 }$ 
B) -2 
C) 4 
D) not geometric 
E) -4

Question 12

Find the sum of the finite geometric sequence.Round to the nearest thousandth. $$\sum _ { i = 0 } ^ { 5 } 600 ( 1.05 ) ^ { i }$$

Accepted Answer

A) 4081.148 
B) 3197.686 
C) 4285.205 
D) 3481.148 
E) 3315.379 
A) 4081.148 
B) 3197.686 
C) 4285.205 
D) 3481.148 
E) 3315.379

Question 13

Find the first five terms of the geometric sequence.? $$a _ { 1 } = 4 , r = e$$ ?

Accepted Answer

A)  $4 , e , 2 e , 3 e , 4 e$ 
B)  $4 , e ^ { 2 } , e ^ { 3 } , e ^ { 4 } , e ^ { 5 }$ 
C)  $e , e , e , e , e$ 
D)  $4 , e , 2 e ^ { 2 } , 3 e ^ { 3 } , 4 e ^ { 4 }$ 
E)  $4,4 e , 4 e ^ { 2 } , 4 e ^ { 3 } , 4 e ^ { 4 }$ 
A)  $4 , e , 2 e , 3 e , 4 e$ 
B)  $4 , e ^ { 2 } , e ^ { 3 } , e ^ { 4 } , e ^ { 5 }$ 
C)  $e , e , e , e , e$ 
D)  $4 , e , 2 e ^ { 2 } , 3 e ^ { 3 } , 4 e ^ { 4 }$ 
E)  $4,4 e , 4 e ^ { 2 } , 4 e ^ { 3 } , 4 e ^ { 4 }$

Question 14

Write the first five terms of the geometric sequence. $$a _ { 1 } = - 5 , r = \frac { 1 } { 8 }$$

Accepted Answer

A)  $- 5 , - \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 } , - \frac { 5 } { 4,096 }$ 
B)  $1 , - 5 , - \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 }$ 
C) -5,-40,-320,-2,560,-20,480 
D) -5,3,11,19,27 
E)  $- \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 } , - \frac { 5 } { 4,096 } , - \frac { 5 } { 32,768 }$ ? 
A)  $- 5 , - \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 } , - \frac { 5 } { 4,096 }$ 
B)  $1 , - 5 , - \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 }$ 
C) -5,-40,-320,-2,560,-20,480 
D) -5,3,11,19,27 
E)  $- \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 } , - \frac { 5 } { 4,096 } , - \frac { 5 } { 32,768 }$ ?

Question 15

Find the sum of the finite geometric sequence.? $$\sum _ { n = 1 } ^ { 7 } 2 ^ { n - 1 }$$ ?

Accepted Answer

A) 43 
B) 22 
C) 127 
D) 63 
E) 31 
A) 43 
B) 22 
C) 127 
D) 63 
E) 31

Question 16

Find the first five terms of the geometric sequence.? $$a _ { 1 } = 6 , r = 2$$ ?

Accepted Answer

A)  $4,8,16,32,64$ 
B)  $5,10,20,40,80$ 
C)  $12,24,48,96,192$ 
D)  $6,12,24,48,96$ 
E)  $10,20,40,80,160$ 
A)  $4,8,16,32,64$ 
B)  $5,10,20,40,80$ 
C)  $12,24,48,96,192$ 
D)  $6,12,24,48,96$ 
E)  $10,20,40,80,160$

Question 17

Use summation notation to write the sum.? $$12 + 36 + 108 + \ldots + 8,748$$ ?

Accepted Answer

A)  $$\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n - 1 }$$ 
B)  $$\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n + 1 }$$ 
C)  $\sum _ { n = 1 } ^ { 6 } 12 ( 3 ) ^ { n - 1 }$ 
D)  $\sum _ { n = 1 } ^ { 7 } 3 ^ { n - 1 }$ 
E)  $\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n }$ 
A)  $$\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n - 1 }$$ 
B)  $$\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n + 1 }$$ 
C)  $\sum _ { n = 1 } ^ { 6 } 12 ( 3 ) ^ { n - 1 }$ 
D)  $\sum _ { n = 1 } ^ { 7 } 3 ^ { n - 1 }$ 
E)  $\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n }$

Question 18

Find the sum using the formulas for the sums of powers of integers. $$\sum _ { n = 1 } ^ { 8 } \left( 7 n - 3 n ^ { 2 } \right)$$

Accepted Answer

A) -224 
B) -1080 
C) -136 
D) 144 
E) -360 
A) -224 
B) -1080 
C) -136 
D) 144 
E) -360

Question 19

Determine whether the sequence is geometric.If so,find the common ratio.? $$7,14,22,70 , \ldots$$ ?

Accepted Answer

A) Geometric sequence, $$r = 1$$ 
B) Geometric sequence, $$r = 2$$ 
C) Geometric sequence, $r = 3$ 
D) Geometric sequence, $r = 4$ 
E) Not a geometric sequence 
A) Geometric sequence, $$r = 1$$ 
B) Geometric sequence, $$r = 2$$ 
C) Geometric sequence, $r = 3$ 
D) Geometric sequence, $r = 4$ 
E) Not a geometric sequence

Question 20

Use summation notation to write the sum.? $$0.9 + 3.6 + 14.4 + \ldots + 921.6$$ ?

Accepted Answer

A)  $\sum _ { n = 1 } ^ { 8 } 0.9 ( 4 ) ^ { n + 1 }$ 
B)  $\sum _ { n = 1 } ^ { 6 } ( 4 ) ^ { n - 1 }$ 
C)  $\sum _ { n = 1 } ^ { 7 } 0.9 ( 4 ) ^ { n - 1 }$ 
D)  $\sum _ { n = 1 } ^ { 8 } 0.9 ( 4 ) ^ { n }$ 
E)  $\sum _ { n = 1 } ^ { 6 } 0.9 ( 4 ) ^ { n - 1 }$ 
A)  $\sum _ { n = 1 } ^ { 8 } 0.9 ( 4 ) ^ { n + 1 }$ 
B)  $\sum _ { n = 1 } ^ { 6 } ( 4 ) ^ { n - 1 }$ 
C)  $\sum _ { n = 1 } ^ { 7 } 0.9 ( 4 ) ^ { n - 1 }$ 
D)  $\sum _ { n = 1 } ^ { 8 } 0.9 ( 4 ) ^ { n }$ 
E)  $\sum _ { n = 1 } ^ { 6 } 0.9 ( 4 ) ^ { n - 1 }$

Exam 54: Geometric Sequences and Series

Find the sum of the finite geometric sequence.(Round your answer to three decimal places. )? ∑n=05300(1.06)n\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }∑n=05​300(1.06)n ?

Find the sum of the finite geometric sequence? ∑n=16(−6)n−1\sum _ { n = 1 } ^ { 6 } ( - 6 ) ^ { n - 1 }∑n=16​(−6)n−1 ?

Write the nth term of the geometric sequence as a function of n. a1=2,ak+1=4aka _ { 1 } = 2 , a _ { k + 1 } = 4 a _ { k }a1​=2,ak+1​=4ak​

Use a graphing utility to graph the first 10 terms of the sequence.? an=3(−0.7)n−1a _ { n } = 3 ( - 0.7 ) ^ { n - 1 }an​=3(−0.7)n−1

Find the indicated nth term of the geometric sequence. ? 22th term : 8,32,128,…8,32,128 , \ldots8,32,128,… ?

Find the sum of the infinite geometric series.? ∑n=0∞(−18)n\sum _ { n = 0 } ^ { \infty } \left( - \frac { 1 } { 8 } \right) ^ { n }∑n=0∞​(−81​)n ?

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places. )? a1=7,r=3,n=8a _ { 1 } = 7 , r = \sqrt { 3 } , n = 8a1​=7,r=3​,n=8 ?

Find the first five terms of the geometric sequence.? a1=4,r=πa _ { 1 } = 4 , r = \pia1​=4,r=π ?

Find the first five terms of the geometric sequence.? a1=5,r=3a _ { 1 } = 5 , r = 3a1​=5,r=3 ?

?Find the sum of the finite geometric sequence. ?? ∑n=110(−34)n−1\sum _ { n = 1 } ^ { 10 } \left( - \frac { 3 } { 4 } \right) ^ { n - 1 }∑n=110​(−43​)n−1 ?

Determine whether the sequence is geometric.If so,find the common ratio. -2,2,6,10,...

Find the sum of the finite geometric sequence.Round to the nearest thousandth. ∑i=05600(1.05)i\sum _ { i = 0 } ^ { 5 } 600 ( 1.05 ) ^ { i }∑i=05​600(1.05)i

Find the first five terms of the geometric sequence.? a1=4,r=ea _ { 1 } = 4 , r = ea1​=4,r=e ?

Write the first five terms of the geometric sequence. a1=−5,r=18a _ { 1 } = - 5 , r = \frac { 1 } { 8 }a1​=−5,r=81​

Find the sum of the finite geometric sequence.? ∑n=172n−1\sum _ { n = 1 } ^ { 7 } 2 ^ { n - 1 }∑n=17​2n−1 ?

Find the first five terms of the geometric sequence.? a1=6,r=2a _ { 1 } = 6 , r = 2a1​=6,r=2 ?

Use summation notation to write the sum.? 12+36+108+…+8,74812 + 36 + 108 + \ldots + 8,74812+36+108+…+8,748 ?

Find the sum using the formulas for the sums of powers of integers. ∑n=18(7n−3n2)\sum _ { n = 1 } ^ { 8 } \left( 7 n - 3 n ^ { 2 } \right)∑n=18​(7n−3n2)

Determine whether the sequence is geometric.If so,find the common ratio.? 7,14,22,70,…7,14,22,70 , \ldots7,14,22,70,… ?

Use summation notation to write the sum.? 0.9+3.6+14.4+…+921.60.9 + 3.6 + 14.4 + \ldots + 921.60.9+3.6+14.4+…+921.6 ?

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Find the sum of the finite geometric sequence.(Round your answer to three decimal places. )? $\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }$ ?

Find the sum of the finite geometric sequence? $\sum _ { n = 1 } ^ { 6 } ( - 6 ) ^ { n - 1 }$ ?

Write the nth term of the geometric sequence as a function of n. $a _ { 1 } = 2 , a _ { k + 1 } = 4 a _ { k }$

Use a graphing utility to graph the first 10 terms of the sequence.? $a _ { n } = 3 ( - 0.7 ) ^ { n - 1 }$

Find the indicated nth term of the geometric sequence. ? 22th term : $8,32,128 , \ldots$ ?

Find the sum of the infinite geometric series.? $\sum _ { n = 0 } ^ { \infty } \left( - \frac { 1 } { 8 } \right) ^ { n }$ ?

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places. )? $a _ { 1 } = 7 , r = \sqrt { 3 } , n = 8$ ?

Find the first five terms of the geometric sequence.? $a _ { 1 } = 4 , r = \pi$ ?

Find the first five terms of the geometric sequence.? $a _ { 1 } = 5 , r = 3$ ?

?Find the sum of the finite geometric sequence. ?? $\sum _ { n = 1 } ^ { 10 } \left( - \frac { 3 } { 4 } \right) ^ { n - 1 }$ ?

Find the sum of the finite geometric sequence.Round to the nearest thousandth. $\sum _ { i = 0 } ^ { 5 } 600 ( 1.05 ) ^ { i }$

Find the first five terms of the geometric sequence.? $a _ { 1 } = 4 , r = e$ ?

Write the first five terms of the geometric sequence. $a _ { 1 } = - 5 , r = \frac { 1 } { 8 }$

Find the sum of the finite geometric sequence.? $\sum _ { n = 1 } ^ { 7 } 2 ^ { n - 1 }$ ?

Find the first five terms of the geometric sequence.? $a _ { 1 } = 6 , r = 2$ ?

Use summation notation to write the sum.? $12 + 36 + 108 + \ldots + 8,748$ ?

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 8 } \left( 7 n - 3 n ^ { 2 } \right)$

Determine whether the sequence is geometric.If so,find the common ratio.? $7,14,22,70 , \ldots$ ?

Use summation notation to write the sum.? $0.9 + 3.6 + 14.4 + \ldots + 921.6$ ?