Question 1

Find the rational number representation of the repeating decimal. $$0.\overline{725}$$

Accepted Answer

A)  $\frac { 725 } { 99 }$ 
B)  $\frac { 999 } { 725 }$ 
C)  $\frac { 725 } { 9 }$ 
D)  $\frac { 725 } { 999 }$ 
E)  $\frac { 725 } { 9999 }$ 
A)  $\frac { 725 } { 99 }$ 
B)  $\frac { 999 } { 725 }$ 
C)  $\frac { 725 } { 9 }$ 
D)  $\frac { 725 } { 999 }$ 
E)  $\frac { 725 } { 9999 }$

Question 2

Write an expression for the nth term of the geometric sequence.Then find the indicated term.? $$a _ { 1 } = 4 , r = \frac { 1 } { 6 } , n = 10$$ ?

Accepted Answer

A)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$ 
B)  $a _ { n } = 4 \left( \frac { 1 } { 6 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$ 
C)  $a _ { n } = 4 \left( \frac { 1 } { 6 } \right) ^ { n + 1 }$ , $\frac { 1 } { 2,519,424 }$ 
D)  $a _ { n } = 6 \left( \frac { 1 } { 2 } \right) ^ { n + 1 }$ , $\frac { 1 } { 2,519,424 }$ 
E)  $a _ { n } = \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$ 
A)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$ 
B)  $a _ { n } = 4 \left( \frac { 1 } { 6 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$ 
C)  $a _ { n } = 4 \left( \frac { 1 } { 6 } \right) ^ { n + 1 }$ , $\frac { 1 } { 2,519,424 }$ 
D)  $a _ { n } = 6 \left( \frac { 1 } { 2 } \right) ^ { n + 1 }$ , $\frac { 1 } { 2,519,424 }$ 
E)  $a _ { n } = \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$

Question 3

Find the indicated nth term of the geometric sequence. ?
7th term : $$3,21,147 , \ldots$$ ?

Accepted Answer

A)  $a _ { 7 } = 50,421$ 
B)  $a _ { 7 } = 7,203$ 
C)  $a _ { 7 } = 17,294,403$ 
D)  $a _ { 7 } = 352,947$ 
E)  $a _ { 7 } = 2,470,629$ 
A)  $a _ { 7 } = 50,421$ 
B)  $a _ { 7 } = 7,203$ 
C)  $a _ { 7 } = 17,294,403$ 
D)  $a _ { 7 } = 352,947$ 
E)  $a _ { 7 } = 2,470,629$

Question 4

Use summation notation to write the sum.? $$8 + 16 + 32 + \ldots + 1024$$ ?

Accepted Answer

A)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n + 1 }$ 
B)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n - 1 }$ 
C)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n }$ 
D)  $$\sum _ { n = 1 } ^ { 7 } 8 ( 2 ) ^ { n - 1 }$$ 
E)  $\sum _ { n = 1 } ^ { 8 } ( 2 ) ^ { n - 1 }$ 
A)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n + 1 }$ 
B)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n - 1 }$ 
C)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n }$ 
D)  $$\sum _ { n = 1 } ^ { 7 } 8 ( 2 ) ^ { n - 1 }$$ 
E)  $\sum _ { n = 1 } ^ { 8 } ( 2 ) ^ { n - 1 }$

Question 5

Find Pk+1 for the given Pk. $$P _ { k } = \frac { 3 } { k ( k + 7 ) }$$

Accepted Answer

A)  $P _ { k + 1 } = \frac { 3 } { k ( k + 7 ) } + 1$ 
B)  $P _ { k + 1 } = \frac { 3 } { k ( k + 7 ) } + \frac { 3 } { ( k + 1 ) ( k + 8 ) }$ 
C)  $P _ { k + 1 } = \frac { 3 } { ( k + 1 ) ( k + 8 ) }$ 
D)  $P _ { k + 1 } = \frac { 3 } { k ( k + 8 ) }$ 
E)  $P _ { k + 1 } = \frac { 8 } { ( k + 1 ) ( k + 7 ) }$ 
A)  $P _ { k + 1 } = \frac { 3 } { k ( k + 7 ) } + 1$ 
B)  $P _ { k + 1 } = \frac { 3 } { k ( k + 7 ) } + \frac { 3 } { ( k + 1 ) ( k + 8 ) }$ 
C)  $P _ { k + 1 } = \frac { 3 } { ( k + 1 ) ( k + 8 ) }$ 
D)  $P _ { k + 1 } = \frac { 3 } { k ( k + 8 ) }$ 
E)  $P _ { k + 1 } = \frac { 8 } { ( k + 1 ) ( k + 7 ) }$

Question 6

Find the sum of the infinite geometric sequence. ​
2 + 0.4 + 0.08 ...
​

Accepted Answer

A) s = 2.5 
B) s = 6.5 
C) s = 0.1 
D) s = 4.5 
E) s = 0.5 
A) s = 2.5 
B) s = 6.5 
C) s = 0.1 
D) s = 4.5 
E) s = 0.5

Question 7

Prove the inequality for the indicated integer values of n. $\left( \frac { 6 } { 5 } \right) ^ { n } > n , n \geq 15$

Accepted Answer

1) @#IMG-DLM& 
.The statement is true fo

Question 8

Write the first four terms of the geometric sequence with the given properties.
​a = 3,r = 2
​Please enter your answer as four numbers in order,separated by commas.

Accepted Answer

The answer of Write the first four terms of the...

Question 9

Find the first five terms of the geometric sequence.? $$a _ { 1 } = 4 , r = 2 x$$ ?

Accepted Answer

A)  $4,2 x , 2 x ^ { 2 } , 2 x ^ { 3 } , 2 x ^ { 4 }$ 
B)  $4,8 x , 16 x ^ { 2 } , 32 x ^ { 3 } , 64 x ^ { 4 }$ 
C)  $4,2 x ^ { 2 } , 2 x ^ { 3 } , 2 x ^ { 4 } , 2 x ^ { 5 }$ 
D)  $4,8 x ^ { 2 } , 16 x ^ { 3 } , 32 x ^ { 4 } , 64 x ^ { 5 }$ 
E)  $4 , x ^ { 2 } , x ^ { 3 } , x ^ { 4 } , x ^ { 5 }$ 
A)  $4,2 x , 2 x ^ { 2 } , 2 x ^ { 3 } , 2 x ^ { 4 }$ 
B)  $4,8 x , 16 x ^ { 2 } , 32 x ^ { 3 } , 64 x ^ { 4 }$ 
C)  $4,2 x ^ { 2 } , 2 x ^ { 3 } , 2 x ^ { 4 } , 2 x ^ { 5 }$ 
D)  $4,8 x ^ { 2 } , 16 x ^ { 3 } , 32 x ^ { 4 } , 64 x ^ { 5 }$ 
E)  $4 , x ^ { 2 } , x ^ { 3 } , x ^ { 4 } , x ^ { 5 }$

Question 10

Find the indicated nth term of the geometric sequence. $$10 \text { th term: } 2 , - 10,50 , \ldots$$

Accepted Answer

A) -5,120 
B) -3,906,250 
C) -2,560 
D) -43 
E) 19,531,250 
A) -5,120 
B) -3,906,250 
C) -2,560 
D) -43 
E) 19,531,250

Question 11

Find the sum of the infinite geometric sequence.? $$\sum _ { n = 1 } ^ { \infty } 8 - \left( \frac { 1 } { 6 } \right) ^ { n - 1 }$$

Accepted Answer

A) ?s = $\frac { 5 } { 34 }$ 
B) ?s = $\frac { 34 } { 5 }$ 
C) ?s = $\frac { 42 } { 5 }$ 
D) ?s = $\frac { 46 } { 5 }$ 
E) ?s = $\frac { 1 } { 5 }$ 
A) ?s = $\frac { 5 } { 34 }$ 
B) ?s = $\frac { 34 } { 5 }$ 
C) ?s = $\frac { 42 } { 5 }$ 
D) ?s = $\frac { 46 } { 5 }$ 
E) ?s = $\frac { 1 } { 5 }$

Question 12

Write an expression for the nth term of the geometric sequence.Then find the indicated term.? $$a _ { 1 } = 6 , r = - \frac { 1 } { 5 } , n = 12$$ ?

Accepted Answer

A)  $a _ { n } = 6 \left( - \frac { 1 } { 5 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$ 
B)  $a _ { n } = 5 \left( - \frac { 1 } { 2 } \right) ^ { n + 1 }$ , $\frac { 6 } { 48,828,125 }$ 
C)  $a _ { n } = 6 \left( - \frac { 1 } { 5 } \right) ^ { n + 1 }$ , $\frac { 6 } { 48,828,125 }$ 
D)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$ 
E)  $a _ { n } = 5 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$ 
A)  $a _ { n } = 6 \left( - \frac { 1 } { 5 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$ 
B)  $a _ { n } = 5 \left( - \frac { 1 } { 2 } \right) ^ { n + 1 }$ , $\frac { 6 } { 48,828,125 }$ 
C)  $a _ { n } = 6 \left( - \frac { 1 } { 5 } \right) ^ { n + 1 }$ , $\frac { 6 } { 48,828,125 }$ 
D)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$ 
E)  $a _ { n } = 5 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$

Question 13

Find the rational number representation of the repeating decimal.? $$0.\overline{859}$$

Accepted Answer

A) ? $\frac { 859 } { 999 }$ 
B) ? $\frac { 859 } { 9 }$ 
C) ? $\frac { 859 } { 9999 }$ 
D) ? $\frac { 85.9 } { 999 }$ 
E) ? $\frac { 859 } { 99 }$ 
A) ? $\frac { 859 } { 999 }$ 
B) ? $\frac { 859 } { 9 }$ 
C) ? $\frac { 859 } { 9999 }$ 
D) ? $\frac { 85.9 } { 999 }$ 
E) ? $\frac { 859 } { 99 }$

Question 14

Find the sum of the infinite geometric series. $$\sum _ { n = 0 } ^ { \infty } - 3 \left( - \frac { 1 } { 5 } \right) ^ { n }$$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  $- \frac { 5 } { 2 }$ 
D)  $- \frac { 1 } { 2 }$ 
E) undefined 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  $- \frac { 5 } { 2 }$ 
D)  $- \frac { 1 } { 2 }$ 
E) undefined

Question 15

Find the sum of the infinite geometric series.? $$\sum _ { n = 0 } ^ { \infty } 7 \left( \frac { 1 } { 3 } \right) ^ { n }$$ ?

Accepted Answer

A) ? $\frac { 2 } { 21 }$ 
B) ? $\frac { 2 } { 7 }$ 
C) ? $- \frac { 1 } { 3 }$ 
D) ? $\frac { 21 } { 2 }$ 
E) ?undefined 
A) ? $\frac { 2 } { 21 }$ 
B) ? $\frac { 2 } { 7 }$ 
C) ? $- \frac { 1 } { 3 }$ 
D) ? $\frac { 21 } { 2 }$ 
E) ?undefined

Question 16

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places. )? $$a _ { 1 } = 900 , r = 1.02 , n = 40$$ ?

Accepted Answer

A)  $a _ { n } = 900 ( 1.02 ) ^ { n + 1 }$ ,About 1948.270 
B)  $a _ { n } = ( 1.02 ) ^ { n - 1 }$ ,About 1948.270 
C)  $a _ { n } = 900 ( 1.02 ) ^ { n - 1 }$ ,About 1948.270 
D)  $a _ { n } = 900 ( 1.02 ) ^ { n - 1 }$ ,About 1987.236 
E)  $a _ { n } = ( 1.02 ) ^ { n + 1 }$ ,About 1948.270 
A)  $a _ { n } = 900 ( 1.02 ) ^ { n + 1 }$ ,About 1948.270 
B)  $a _ { n } = ( 1.02 ) ^ { n - 1 }$ ,About 1948.270 
C)  $a _ { n } = 900 ( 1.02 ) ^ { n - 1 }$ ,About 1948.270 
D)  $a _ { n } = 900 ( 1.02 ) ^ { n - 1 }$ ,About 1987.236 
E)  $a _ { n } = ( 1.02 ) ^ { n + 1 }$ ,About 1948.270

Question 17

A principal of $2500 is invested at 2% interest.Find the amount after 20 years if the interest is compounded quarterly. ​

Accepted Answer

A) $3724.85 
B) $3727.85 
C) $3723.85 
D) $3726.85 
E) $3725.85 
A) $3724.85 
B) $3727.85 
C) $3723.85 
D) $3726.85 
E) $3725.85

Question 18

Determine whether the sequence is geometric.If so,find the common ratio.? $$7,1.4,0.28,0.056 , \ldots$$ ?

Accepted Answer

A) Geometric sequence, $r = 0.5$ 
B) Geometric sequence, $r = 0.2$ 
C) Geometric sequence, $r = 0.4$ 
D) Not a geometric sequence 
E) Geometric sequence, $r = 0.3$ 
A) Geometric sequence, $r = 0.5$ 
B) Geometric sequence, $r = 0.2$ 
C) Geometric sequence, $r = 0.4$ 
D) Not a geometric sequence 
E) Geometric sequence, $r = 0.3$

Question 19

Find the indicated nth term of the geometric sequence. ?
9th term : $$13,39,117 , \ldots$$ ?

Accepted Answer

A)  $a _ { 9 } = 3,159$ 
B)  $a _ { 9 } = 255,879$ 
C)  $a _ { 9 } = 28,431$ 
D)  $a _ { 9 } = 85,293$ 
E)  $a _ { 9 } = 9,477$ 
A)  $a _ { 9 } = 3,159$ 
B)  $a _ { 9 } = 255,879$ 
C)  $a _ { 9 } = 28,431$ 
D)  $a _ { 9 } = 85,293$ 
E)  $a _ { 9 } = 9,477$

Question 20

Find a quadratic model for the sequence with the indicated terms. $$a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31$$

Accepted Answer

A)  $a _ { n } = 3 n ^ { 2 } + 3$ 
B)  $a _ { n } = 3 n ^ { 2 } - 5 n + 3$ 
C)  $a _ { n } = 3 n ^ { 2 } - 3 n + 3$ 
D)  $a _ { n } = 3 n ^ { 2 } - 3 n + 5$ 
E)  $a _ { n } = n ^ { 2 } + 5 n + 3$ 
A)  $a _ { n } = 3 n ^ { 2 } + 3$ 
B)  $a _ { n } = 3 n ^ { 2 } - 5 n + 3$ 
C)  $a _ { n } = 3 n ^ { 2 } - 3 n + 3$ 
D)  $a _ { n } = 3 n ^ { 2 } - 3 n + 5$ 
E)  $a _ { n } = n ^ { 2 } + 5 n + 3$

Exam 54: Geometric Sequences and Series

Find the rational number representation of the repeating decimal. 0.725‾0.\overline{725}0.725

Write an expression for the nth term of the geometric sequence.Then find the indicated term.? a1=4,r=16,n=10a _ { 1 } = 4 , r = \frac { 1 } { 6 } , n = 10a1​=4,r=61​,n=10 ?

Find the indicated nth term of the geometric sequence. ? 7th term : 3,21,147,…3,21,147 , \ldots3,21,147,… ?

Use summation notation to write the sum.? 8+16+32+…+10248 + 16 + 32 + \ldots + 10248+16+32+…+1024 ?

Find Pk+1 for the given Pk. Pk=3k(k+7)P _ { k } = \frac { 3 } { k ( k + 7 ) }Pk​=k(k+7)3​

Find the sum of the infinite geometric sequence. ​ 2 + 0.4 + 0.08 ... ​

Prove the inequality for the indicated integer values of n. (65)n>n,n≥15\left( \frac { 6 } { 5 } \right) ^ { n } > n , n \geq 15(56​)n>n,n≥15

Write the first four terms of the geometric sequence with the given properties. ​a = 3,r = 2 ​Please enter your answer as four numbers in order,separated by commas.

Find the first five terms of the geometric sequence.? a1=4,r=2xa _ { 1 } = 4 , r = 2 xa1​=4,r=2x ?

Find the indicated nth term of the geometric sequence. 10 th term: 2,−10,50,…10 \text { th term: } 2 , - 10,50 , \ldots10 th term: 2,−10,50,…

Find the sum of the infinite geometric sequence.? ∑n=1∞8−(16)n−1\sum _ { n = 1 } ^ { \infty } 8 - \left( \frac { 1 } { 6 } \right) ^ { n - 1 }∑n=1∞​8−(61​)n−1

Write an expression for the nth term of the geometric sequence.Then find the indicated term.? a1=6,r=−15,n=12a _ { 1 } = 6 , r = - \frac { 1 } { 5 } , n = 12a1​=6,r=−51​,n=12 ?

Find the rational number representation of the repeating decimal.? 0.859‾0.\overline{859}0.859

Find the sum of the infinite geometric series. ∑n=0∞−3(−15)n\sum _ { n = 0 } ^ { \infty } - 3 \left( - \frac { 1 } { 5 } \right) ^ { n }∑n=0∞​−3(−51​)n

Find the sum of the infinite geometric series.? ∑n=0∞7(13)n\sum _ { n = 0 } ^ { \infty } 7 \left( \frac { 1 } { 3 } \right) ^ { n }∑n=0∞​7(31​)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=900,r=1.02,n=40a _ { 1 } = 900 , r = 1.02 , n = 40a1​=900,r=1.02,n=40 ?

A principal of $2500 is invested at 2% interest.Find the amount after 20 years if the interest is compounded quarterly. ​

Determine whether the sequence is geometric.If so,find the common ratio.? 7,1.4,0.28,0.056,…7,1.4,0.28,0.056 , \ldots7,1.4,0.28,0.056,… ?

Find the indicated nth term of the geometric sequence. ? 9th term : 13,39,117,…13,39,117 , \ldots13,39,117,… ?

Find a quadratic model for the sequence with the indicated terms. a0=3,a1=1,a4=31a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31a0​=3,a1​=1,a4​=31

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 rational number representation of the repeating decimal. $0.\overline{725}$

Write an expression for the nth term of the geometric sequence.Then find the indicated term.? $a _ { 1 } = 4 , r = \frac { 1 } { 6 } , n = 10$ ?

Find the indicated nth term of the geometric sequence. ? 7th term : $3,21,147 , \ldots$ ?

Use summation notation to write the sum.? $8 + 16 + 32 + \ldots + 1024$ ?

Find Pk₊₁ for the given P_k. $P _ { k } = \frac { 3 } { k ( k + 7 ) }$

Find the sum of the infinite geometric sequence. 2 + 0.4 + 0.08 ...

Prove the inequality for the indicated integer values of n. $\left( \frac { 6 } { 5 } \right) ^ { n } > n , n \geq 15$

Write the first four terms of the geometric sequence with the given properties. a = 3,r = 2 Please enter your answer as four numbers in order,separated by commas.

Find the first five terms of the geometric sequence.? $a _ { 1 } = 4 , r = 2 x$ ?

Find the indicated nth term of the geometric sequence. $10 \text { th term: } 2 , - 10,50 , \ldots$

Find the sum of the infinite geometric sequence.? $\sum _ { n = 1 } ^ { \infty } 8 - \left( \frac { 1 } { 6 } \right) ^ { n - 1 }$

Write an expression for the nth term of the geometric sequence.Then find the indicated term.? $a _ { 1 } = 6 , r = - \frac { 1 } { 5 } , n = 12$ ?

Find the rational number representation of the repeating decimal.? $0.\overline{859}$

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } - 3 \left( - \frac { 1 } { 5 } \right) ^ { n }$

Find the sum of the infinite geometric series.? $\sum _ { n = 0 } ^ { \infty } 7 \left( \frac { 1 } { 3 } \right) ^ { n }$ ?

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places. )? $a _ { 1 } = 900 , r = 1.02 , n = 40$ ?

A principal of $2500 is invested at 2% interest.Find the amount after 20 years if the interest is compounded quarterly.

Determine whether the sequence is geometric.If so,find the common ratio.? $7,1.4,0.28,0.056 , \ldots$ ?

Find the indicated nth term of the geometric sequence. ? 9th term : $13,39,117 , \ldots$ ?

Find a quadratic model for the sequence with the indicated terms. $a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31$