Question 1

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$2,6,10,14,18 , \ldots$$ ​

Accepted Answer

A)  $$a _ { n } = 2 n - 4$$ 
B)  $a _ { n } = 4 n - 2$ 
C)  $$a _ { n } = 2 n + 4$$ 
D)  $a _ { n } = - 4 n - 2$ 
E)  $a _ { n } = 4 n + 2$ 
A)  $$a _ { n } = 2 n - 4$$ 
B)  $a _ { n } = 4 n - 2$ 
C)  $$a _ { n } = 2 n + 4$$ 
D)  $a _ { n } = - 4 n - 2$ 
E)  $a _ { n } = 4 n + 2$

Question 2

Find the indicated partial sum of the series. $$\sum _ { i = 1 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { i }$$ fourth partial sum

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  $- \frac { 17 } { 12 }$ ​ 
C)  $\frac { 11 } { 4 }$ ​ 
D)  $\frac { 1 } { 4 }$ ​ 
E)  $- \frac { 5 } { 4 }$ ​ 
A)  $\frac { 3 } { 4 }$ 
B)  $- \frac { 17 } { 12 }$ ​ 
C)  $\frac { 11 } { 4 }$ ​ 
D)  $\frac { 1 } { 4 }$ ​ 
E)  $- \frac { 5 } { 4 }$ ​

Question 3

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = 5 n - 6$$ ​

Accepted Answer

A)  $0 , - 1,4,9,14$ 
B)  $- 1,4,9,14,19$ 
C)  $5 , - 1,15,9,25$ 
D)  $5,10,15,20,25$ 
E)  $5,4,15,14,25$ 
A)  $0 , - 1,4,9,14$ 
B)  $- 1,4,9,14,19$ 
C)  $5 , - 1,15,9,25$ 
D)  $5,10,15,20,25$ 
E)  $5,4,15,14,25$

Question 4

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = \frac { n } { n + 7 }$$ ​

Accepted Answer

A)  $- 8 , \frac { 9 } { 2 } , - \frac { 10 } { 3 } , \frac { 11 } { 4 } , - \frac { 12 } { 5 }$ ​ 
B)  $8 , - \frac { 9 } { 2 } , - \frac { 10 } { 3 } , - \frac { 11 } { 4 } , - \frac { 12 } { 5 }$ ​ 
C)  $8 , \frac { 9 } { 2 } , \frac { 10 } { 3 } , \frac { 11 } { 4 } , \frac { 12 } { 5 }$ ​ 
D)  $\frac { 1 } { 8 } , \frac { 2 } { 9 } , \frac { 3 } { 10 } , \frac { 4 } { 11 } , \frac { 5 } { 12 }$ ​ 
E)  $0 , \frac { 1 } { 8 } , \frac { 2 } { 9 } , \frac { 3 } { 10 } , \frac { 4 } { 11 }$ ​ 
A)  $- 8 , \frac { 9 } { 2 } , - \frac { 10 } { 3 } , \frac { 11 } { 4 } , - \frac { 12 } { 5 }$ ​ 
B)  $8 , - \frac { 9 } { 2 } , - \frac { 10 } { 3 } , - \frac { 11 } { 4 } , - \frac { 12 } { 5 }$ ​ 
C)  $8 , \frac { 9 } { 2 } , \frac { 10 } { 3 } , \frac { 11 } { 4 } , \frac { 12 } { 5 }$ ​ 
D)  $\frac { 1 } { 8 } , \frac { 2 } { 9 } , \frac { 3 } { 10 } , \frac { 4 } { 11 } , \frac { 5 } { 12 }$ ​ 
E)  $0 , \frac { 1 } { 8 } , \frac { 2 } { 9 } , \frac { 3 } { 10 } , \frac { 4 } { 11 }$ ​

Question 5

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) $$a _ { 1 } = 7 , a _ { k + 1 } = a _ { k } - 1$$

Accepted Answer

A)  $a _ { n } = 8 - n ; 7,6,5,4,3$ ​ 
B)  $a _ { n } = 7 ; 7,7,7,7,7$ ​ 
C)  $a _ { n } = 9 - n ; 6,5,4,3,2$ ​ 
D)  $a _ { n } = 8 n ; 7,21,28,35,42$ ​ 
E)  $a _ { n } = 7 ( n - 1 ) ; 7,14,21,28,35$ ​ 
A)  $a _ { n } = 8 - n ; 7,6,5,4,3$ ​ 
B)  $a _ { n } = 7 ; 7,7,7,7,7$ ​ 
C)  $a _ { n } = 9 - n ; 6,5,4,3,2$ ​ 
D)  $a _ { n } = 8 n ; 7,21,28,35,42$ ​ 
E)  $a _ { n } = 7 ( n - 1 ) ; 7,14,21,28,35$ ​

Question 6

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$3,5,3,5,3 , \ldots$$ ​

Accepted Answer

A)  $a _ { n } = ( - 1 ) ^ { n } + 4$ 
B)  $a _ { n } = ( - 1 ) ^ { n + 1 }$ 
C)  $a _ { n } = ( - 1 ) ^ { n } - 4$ 
D)  $a _ { n } = 4 ^ { n } - 1$ 
E)  $a _ { n } = ( - 1 ) ^ { n - 1 } + 4$ 
A)  $a _ { n } = ( - 1 ) ^ { n } + 4$ 
B)  $a _ { n } = ( - 1 ) ^ { n + 1 }$ 
C)  $a _ { n } = ( - 1 ) ^ { n } - 4$ 
D)  $a _ { n } = 4 ^ { n } - 1$ 
E)  $a _ { n } = ( - 1 ) ^ { n - 1 } + 4$

Question 7

Find the sum of the infinite series.​ $$\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 10 } \right) ^ { i }$$ ​

Accepted Answer

A)  $\frac { 2 } { 9 }$ ​ 
B)  $\frac { 9 k } { 2 }$ ​ 
C)  $\frac { 9 } { 2 }$ ​ 
D)  $- \frac { 2 k } { 9 }$ ​ 
E)  $\frac { 2 k } { 9 }$ ​ 
A)  $\frac { 2 } { 9 }$ ​ 
B)  $\frac { 9 k } { 2 }$ ​ 
C)  $\frac { 9 } { 2 }$ ​ 
D)  $- \frac { 2 k } { 9 }$ ​ 
E)  $\frac { 2 k } { 9 }$ ​

Question 8

A deposit of $ 5000 is made in an account that earns 8 % interest compounded monthly.The balance in the account after n months is given by $$A _ { n } = 5000 \left( 1 + \frac { 0.08 } { 12 } \right) ^ { n } , n = 1,2,3 , \ldots$$ Find the balance in the account after 8 years by finding the 96th term of the sequence.Round to the nearest penny.

Accepted Answer

A) $ 8,084,450.96 
B) $ 9462.29 
C) $ 9399.62 
D) $ 483200.00 
E) $ 9525.37 
A) $ 8,084,450.96 
B) $ 9462.29 
C) $ 9399.62 
D) $ 483200.00 
E) $ 9525.37

Question 9

​Simplify the factorial expression. $\frac { 12 ! } { 9 ! }$ ​

Accepted Answer

A) ​$11880 
B) ​1320 
C) ​ $\frac { 4 } { 3 }$ 
D) ​132 
E) ​$17160 
A) ​$11880 
B) ​1320 
C) ​ $\frac { 4 } { 3 }$ 
D) ​132 
E) ​$17160

Question 10

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) 3,8,13,18,23

Accepted Answer

A)  $a _ { n } = - 2 n + 5$ 
B)  $a _ { n } = ( - 1 ) ^ { n } ( 5 n - 2 )$ 
C)  $a _ { n } = 5 n$ 
D)  $a _ { n } = 5 ^ { n } - 2$ 
E)  $a _ { n } = 5 n - 2$ 
A)  $a _ { n } = - 2 n + 5$ 
B)  $a _ { n } = ( - 1 ) ^ { n } ( 5 n - 2 )$ 
C)  $a _ { n } = 5 n$ 
D)  $a _ { n } = 5 ^ { n } - 2$ 
E)  $a _ { n } = 5 n - 2$

Question 11

Find the sum.​ $$\sum _ { i = 1 } ^ { 5 } 6 i ^ { 2 }$$ ​

Accepted Answer

A) 150 
B) 300 
C) 210 
D) 270 
E) 330 
A) 150 
B) 300 
C) 210 
D) 270 
E) 330

Question 12

Find the sum.​ $$\sum _ { i = 1 } ^ { 4 } 50$$ ​

Accepted Answer

A) 200 
B) 199 
C) 210 
D) 201 
E) 150 
A) 200 
B) 199 
C) 210 
D) 201 
E) 150

Question 13

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = \frac { n + 11 } { n }$$ ​

Accepted Answer

A)  $11,12 , \frac { 13 } { 2 } , \frac { 14 } { 3 } , \frac { 15 } { 4 }$ 
B)  $- 12 , \frac { 13 } { 2 } , - \frac { 14 } { 3 } , \frac { 15 } { 4 } , - \frac { 16 } { 5 }$ 
C)  $12 , - \frac { 13 } { 2 } , - \frac { 14 } { 3 } , - \frac { 15 } { 4 } , - \frac { 16 } { 5 }$ 
D)  $12 , \frac { 13 } { 2 } , \frac { 14 } { 3 } , \frac { 15 } { 4 } , \frac { 16 } { 5 }$ 
E)  $\frac { 1 } { 12 } , \frac { 1 } { 13 } , \frac { 1 } { 14 } , \frac { 1 } { 15 } , \frac { 1 } { 16 }$ 
A)  $11,12 , \frac { 13 } { 2 } , \frac { 14 } { 3 } , \frac { 15 } { 4 }$ 
B)  $- 12 , \frac { 13 } { 2 } , - \frac { 14 } { 3 } , \frac { 15 } { 4 } , - \frac { 16 } { 5 }$ 
C)  $12 , - \frac { 13 } { 2 } , - \frac { 14 } { 3 } , - \frac { 15 } { 4 } , - \frac { 16 } { 5 }$ 
D)  $12 , \frac { 13 } { 2 } , \frac { 14 } { 3 } , \frac { 15 } { 4 } , \frac { 16 } { 5 }$ 
E)  $\frac { 1 } { 12 } , \frac { 1 } { 13 } , \frac { 1 } { 14 } , \frac { 1 } { 15 } , \frac { 1 } { 16 }$

Question 14

Find the indicated term of the sequence. $a _ { n } = ( - 1 ) ^ { n } ( 4 n - 1 )$ $a _ { 14 } =$ $\square$

Accepted Answer

A) 57 
B) 52 
C) -3 
D) 55 
E) -51 
A) 57 
B) 52 
C) -3 
D) 55 
E) -51

Question 15

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }$$ ​

Accepted Answer

A)  $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n } }$ 
B)  $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n - 1 } }$ 
C)  $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n + 1 } }$ 
D)  $a _ { n } = \frac { 4 ^ { n } } { 5 ^ { n } }$ 
E)  $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n } }$ 
A)  $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n } }$ 
B)  $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n - 1 } }$ 
C)  $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n + 1 } }$ 
D)  $a _ { n } = \frac { 4 ^ { n } } { 5 ^ { n } }$ 
E)  $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n } }$

Question 16

Find the sum.​ $$\sum _ { i = 1 } ^ { 5 } ( 6 i + 1 )$$ ​

Accepted Answer

A) 85 
B) 35 
C) 26 
D) 95 
E) 55 
A) 85 
B) 35 
C) 26 
D) 95 
E) 55

Question 17

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = ( - 5 ) ^ { n }$$ ​

Accepted Answer

A)  $$- 5,25 , - 15,625 , - 25$$ 
B)  $$- 5,25 , - 125,625 , - 3125$$ 
C)  $1 , - 5,25 , - 125,625$ 
D)  $- 5 , - 10 , - 15 , - 125 , - 25$ 
E)  $- 5 , - 10 , - 15 , - 20 , - 25$ 
A)  $$- 5,25 , - 15,625 , - 25$$ 
B)  $$- 5,25 , - 125,625 , - 3125$$ 
C)  $1 , - 5,25 , - 125,625$ 
D)  $- 5 , - 10 , - 15 , - 125 , - 25$ 
E)  $- 5 , - 10 , - 15 , - 20 , - 25$

Question 18

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$- 2,1,6,13,22 , \ldots$$ ​

Accepted Answer

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

Question 19

Use sigma notation to write the sum. $$\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }$$

Accepted Answer

A)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
B)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { n ( n + 1 ) }$ 
C)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 2 ) ! }$ 
D)  $\sum _ { n = 1 } ^ { 4 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
E)  $\sum _ { n = 0 } ^ { 5 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
A)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
B)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { n ( n + 1 ) }$ 
C)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 2 ) ! }$ 
D)  $\sum _ { n = 1 } ^ { 4 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
E)  $\sum _ { n = 0 } ^ { 5 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$

Question 20

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) $$a _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }$$

Accepted Answer

A)  $a _ { n } = - 7 n ; - 7 , - 21 , - 63 , - 189 , - 567$ ​ 
B)  $$a _ { n } = - 7 ( 3 ) ^ { n } ; - 21 , - 63 , - 189 , - 567 , - 1701$$ ​ 
C)  $a _ { n } = ( - 21 ) ^ { n } ; - 7 , - 63 , - 189 , - 567 , - 1701$ ​ 
D)  $a _ { n } = ( - 21 ) ^ { n - 1 } ; - 21 , - 63 , - 189 , - 567 , - 1701$ ​ 
E)  $a _ { n } = - 7 ( 3 ) ^ { n - 1 } ; - 7 , - 21 , - 63 , - 189 , - 567$ ​ 
A)  $a _ { n } = - 7 n ; - 7 , - 21 , - 63 , - 189 , - 567$ ​ 
B)  $$a _ { n } = - 7 ( 3 ) ^ { n } ; - 21 , - 63 , - 189 , - 567 , - 1701$$ ​ 
C)  $a _ { n } = ( - 21 ) ^ { n } ; - 7 , - 63 , - 189 , - 567 , - 1701$ ​ 
D)  $a _ { n } = ( - 21 ) ^ { n - 1 } ; - 21 , - 63 , - 189 , - 567 , - 1701$ ​ 
E)  $a _ { n } = - 7 ( 3 ) ^ { n - 1 } ; - 7 , - 21 , - 63 , - 189 , - 567$ ​

Exam 52: Sequences and Series

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ 2,6,10,14,18,…2,6,10,14,18 , \ldots2,6,10,14,18,… ​

Find the indicated partial sum of the series. ∑i=1∞4(−12)i\sum _ { i = 1 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { i }∑i=1∞​4(−21​)i fourth partial sum

Select the first five terms of the sequence.(Assume that n begins with 1. )​ an=5n−6a _ { n } = 5 n - 6an​=5n−6 ​

Select the first five terms of the sequence.(Assume that n begins with 1. )​ an=nn+7a _ { n } = \frac { n } { n + 7 }an​=n+7n​ ​

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) a1=7,ak+1=ak−1a _ { 1 } = 7 , a _ { k + 1 } = a _ { k } - 1a1​=7,ak+1​=ak​−1

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ 3,5,3,5,3,…3,5,3,5,3 , \ldots3,5,3,5,3,… ​

Find the sum of the infinite series.​ ∑i=1∞2(110)i\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 10 } \right) ^ { i }∑i=1∞​2(101​)i ​

​Simplify the factorial expression. 12!9!\frac { 12 ! } { 9 ! }9!12!​ ​

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) 3,8,13,18,23

Find the sum.​ ∑i=156i2\sum _ { i = 1 } ^ { 5 } 6 i ^ { 2 }∑i=15​6i2 ​

Find the sum.​ ∑i=1450\sum _ { i = 1 } ^ { 4 } 50∑i=14​50 ​

Select the first five terms of the sequence.(Assume that n begins with 1. )​ an=n+11na _ { n } = \frac { n + 11 } { n }an​=nn+11​ ​

Find the indicated term of the sequence. an=(−1)n(4n−1)a _ { n } = ( - 1 ) ^ { n } ( 4 n - 1 )an​=(−1)n(4n−1) a14=a _ { 14 } =a14​= □\square□

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ 15,425,16125,64625\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }51​,254​,12516​,62564​ ​

Find the sum.​ ∑i=15(6i+1)\sum _ { i = 1 } ^ { 5 } ( 6 i + 1 )∑i=15​(6i+1) ​

Select the first five terms of the sequence.(Assume that n begins with 1. )​ an=(−5)na _ { n } = ( - 5 ) ^ { n }an​=(−5)n ​

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ −2,1,6,13,22,…- 2,1,6,13,22 , \ldots−2,1,6,13,22,… ​

Use sigma notation to write the sum. 13⋅2+14⋅3+…+18⋅7\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }3⋅21​+4⋅31​+…+8⋅71​

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) a1=−7,ak+1=3aka _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }a1​=−7,ak+1​=3ak​

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

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) $2,6,10,14,18 , \ldots$

Find the indicated partial sum of the series. $\sum _ { i = 1 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { i }$ fourth partial sum

Select the first five terms of the sequence.(Assume that n begins with 1. ) $a _ { n } = 5 n - 6$

Select the first five terms of the sequence.(Assume that n begins with 1. ) $a _ { n } = \frac { n } { n + 7 }$

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) $a _ { 1 } = 7 , a _ { k + 1 } = a _ { k } - 1$

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) $3,5,3,5,3 , \ldots$

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 10 } \right) ^ { i }$

Simplify the factorial expression. $\frac { 12 ! } { 9 ! }$

Find the sum. $\sum _ { i = 1 } ^ { 5 } 6 i ^ { 2 }$

Find the sum. $\sum _ { i = 1 } ^ { 4 } 50$

Select the first five terms of the sequence.(Assume that n begins with 1. ) $a _ { n } = \frac { n + 11 } { n }$

Find the indicated term of the sequence. $a _ { n } = ( - 1 ) ^ { n } ( 4 n - 1 )$ $a _ { 14 } =$ $\square$

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) $\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }$

Find the sum. $\sum _ { i = 1 } ^ { 5 } ( 6 i + 1 )$

Select the first five terms of the sequence.(Assume that n begins with 1. ) $a _ { n } = ( - 5 ) ^ { n }$

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) $- 2,1,6,13,22 , \ldots$

Use sigma notation to write the sum. $\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }$

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) $a _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }$