Deck 12: Sequences, Series, and Probability

Question 1

Write the word or phrase that best completes each statement or answers the question.
Consider the following squares. For the nth square, the length of each side is n.
i)Find the areas of the first 4 squares, then list the areas in a sequence.
ii)Find the general term for the area of the nth square in the sequence. Usee for t for the area.

Answer 1

Question 2

Write the first five terms of the sequence whose nth term is shown.

- $a _ { n } = \frac { 3 } { n ^ { 2 } }$

A) $1 , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 }$
B) $1 , \frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 1 } { 4 } , \frac { 1 } { 5 }$
C) $3 , \frac { 3 } { 4 } , \frac { 1 } { 3 } , \frac { 3 } { 16 } , \frac { 3 } { 25 }$
D) $\frac { 1 } { 4 } , \frac { 2 } { 9 } , \frac { 3 } { 16 } , \frac { 4 } { 25 } , \frac { 5 } { 36 }$

Answer 2

$3 , \frac { 3 } { 4 } , \frac { 1 } { 3 } , \frac { 3 } { 16 } , \frac { 3 } { 25 }$

Question 3

Write the first five terms of the sequence whose nth term is shown.

- $a _ { n } = 4 ( 4 n - 1 )$

A)3, 7, 11, 15, 19
B)12, 24, 36, 48, 60
C) $12,28,44,60,76$
D) $- 4,12,28,44,60$

Answer 3

$12,28,44,60,76$

Question 4

Write the first five terms of the sequence whose nth term is shown.

- $a _ { n } = \frac { n } { n ^ { 2 } + 2 }$

A) $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 } , \frac { 5 } { 27 }$
B) $\frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$
C) $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$
D) $\frac { 1 } { 4 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$

Question 5

Write out the series.

- $$\sum _ { n = 1 } ^ { 4 } ( n + 3 )$$

A)7 + 8 + 9 + 10
B)4 + 5 + 6 + 7 + ...
C)3 + 4 + 5 + 6
D)4 + 5 + 6 + 7

Question 6

Evalutate the series.

- $$\sum _ { n = 2 } ^ { 5 } ( 3 n - 3 )$$

A)27
B)24
C)30
D)18

Question 7

Write out the series.

- $\sum _ { n = 1 } ^ { 5 } \frac { n + 1 } { n + 2 }$

A) $\frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 }$
B) $\frac { 6 } { 7 }$
C) $\frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 }$
D) $\frac { 1 } { 3 } + \frac { 2 } { 4 } + \frac { 3 } { 5 } + \frac { 4 } { 6 }$

Question 8

Write the first five terms of the sequence whose nth term is shown.

- $a _ { n } = 3 ^ { n }$

A)1, 3, 9, 27, 81
B)1, 8, 27, 64, 125
C)9, 27, 81, 243, 729
D)3, 9, 27, 81, 243

Question 9

Write the first five terms of the sequence whose nth term is shown.

- $a _ { n } = 2 n - 2$

A)0, 1, 2, 3, 4
B)0, -2, -4, -6, -8
C)0, 2, 4, 6, 8
D)4, 6, 8, 10, 12

Question 10

Write the first five terms of the sequence whose nth term is shown.

- $a _ { n } = ( - 4 ) ^ { n }$

A)16, -64, 256, -1024, 4096
B)-4, 16, -64, 256, -1024
C)4, 16, 64, 256, 1024
D)-4, -8, -12, -16, -20

Question 11

Write the first five terms of the sequence whose nth term is shown.

- $a _ { n } = n - 6$

A)-24, -18, -12, -6, 0
B)1, 2, 3, 4, 5
C)-6, -5, -4, -3, -2
D)-5, -4, -3, -2, -1

Question 12

Write the first five terms of the sequence whose nth term is shown.

- $a _ { n } = n ^ { 2 } - n$

A)0, 3, 8, 15, 24
B)1, 4, 9, 16, 25
C)0, 2, 6, 12, 20
D)2, 6, 12, 20, 30

Question 13

Write the next three terms of the sequence.
5, 9, 13, 17, ...

A)25, 29, 33
B)13, 9, 5
C)21, 25, 29
D)21, 25, 33

Question 14

Find the indicated term of the sequence whose nth term is shown.

- $a _ { n } = \frac { n } { 2 } - 5 \text {, eighth term }$

A)-1
B)9
C)3
D)11

Question 15

Write the next three terms of the sequence.

- $\frac { 3 } { 4 } , - \frac { 1 } { 4 } , \frac { 1 } { 12 } , - \frac { 1 } { 36 } ,.$ , . . .

A) $- \frac { 1 } { 108 } , \frac { 1 } { 324 } , - \frac { 1 } { 972 }$
B) $\frac { 1 } { 36 } , - \frac { 1 } { 48 } , \frac { 1 } { 60 }$
C) $\frac { 1 } { 108 } , - \frac { 1 } { 324 } , \frac { 1 } { 972 }$
D) $- \frac { 1 } { 36 } , \frac { 1 } { 48 } , - \frac { 1 } { 60 }$

Question 16

Write the next three terms of the sequence.
3, 1, -1, -3, ...

A)-5, -7, -9
B)-1, 1, 3
C)5, 7, 9
D)-7, -9, -11

Question 17

Find the indicated term of the sequence whose nth term is shown.

- $a _ { n } = n ( n - 1 ) , \quad \text { eighth term }$

A)240
B)224
C)256
D)16

Question 18

Write out the series.

- $$\sum _ { n = 1 } ^ { 6 } ( 4 n - 3 )$$

A)45
B)1 + 5 + 9 + 13 + 17 + 21 + ...
C)1 + 1 + 5 + 9 + 13 + 17
D)1 + 5 + 9 + 13 + 17 + 21

Question 19

Write the next three terms of the sequence.
4, 16, 64, 256, . . .

A)1024, 4096, 16,384
B)4096, 16,384, 65,536
C)1280, 1536, 1792
D)1025, 4097, 16,385

Question 20

Find the indicated term of the sequence whose nth term is shown.

- $a _ { n } = 2 n - 3 , \text { twelfth term }$

A)35
B)33
C)39
D)36

Question 21

Evalutate the series.

- $$\sum _ { n = 1 } ^ { 4 } \left( - \frac { 1 } { 4 } \right) ^ { n }$$

A) $- \frac { 47 } { 256 }$
B) $\frac { 85 } { 256 }$
C) $- \frac { 51 } { 256 }$
D) $\frac { 51 } { 256 }$

Question 22

Find the first and third partial sums, s1 and s3, for the sequence

- $$a _ { n } = 3 ^ { n } - 6$$

A)-3, 33
B)-3, 9
C)-3, 21
D)-3, 0

Question 23

Evalutate the series.

- $$\sum _ { n = 1 } ^ { 4 } 2 ^ { n }$$

A)18
B)20
C)14
D)30

Question 24

Evalutate the series.

- $$\sum _ { n = 4 } ^ { 7 } 7 n$$

A)105
B)154
C)49
D)77

Question 25

Evalutate the series.

- $$\sum _ { i = 2 } ^ { 4 } n ( n - 10 )$$

A)-70
B)-40
C)-12
D)-61

Question 26

Find the arithmetic meaic mean $\bar { x },$ , of , ofthe following set of data.

-3, 9, 27, 81, 243

A)90.75
B)363
C)72.6
D)60.5

Question 27

Find the arithmetic meaic mean $\bar { x },$ , of , ofthe following set of data.

-10, 20, 30, 40, 50

A)30
B)150
C)40
D)20

Question 28

Find the common difference of the sequence.

- $a _ { 1 } = 5 , a _ { 4 } = 11 ; \text { find } d$

A)6
B)5
C)1.5
D)2

Question 29

For the set of valueses $x _ { 1 } = 1 , x _ { 2 } = 3 , x _ { 3 } = - 2,$ 2, a nd x4 = 6, find the following.

- $\sum _ { i = 1 } ^ { 4 } x _ { i } ^ { 2 } - 2$

A)6
B)42
C)32
D)-10

Question 30

Find the first and third partial sums, s1 and s3, for the sequence

- $$a _ { n } = ( - 2 ) ^ { n }$$

A)-2, -6
B)-2, 2
C)-2, -8
D)-2, -14

Question 31

For the given general term an, write an expression using $\Sigma$ to represent the indicated p to represent the indicated partial sum.

- $a _ { n } = n ^ { 7 },$ fifth partial sum

A) $\sum _ { i = 1 } ^ { 4 } i ^ { 7 }$
B) $\sum _ { i = 0 } ^ { 4 } i ^ { 7 }$
C) $\sum _ { \mathrm { i } = 1 } ^ { 5 } \mathrm { i } ^ { 7 }$
D) $\sum _ { \mathrm { i } = 0 } ^ { 5 } \mathrm { i } ^ { 7 }$

Question 32

Find the arithmetic meaic mean $\bar { x },$ , of , ofthe following set of data.

-1, 4, 7, 10, 13

A)8.75
B)7
C)5.83
D)35

Question 33

Find the first and third partial sums, s1 and s3, for the sequence

- $a _ { n } = \frac { n ^ { 2 } } { n + 4 }$

A) $\frac { 1 } { 5 } , \frac { 9 } { 7 }$
B) $\frac { 1 } { 5 } , \frac { 1 } { 15 }$
C) $\frac { 1 } { 5 } , \frac { 226 } { 105 }$
D) $\frac { 1 } { 5 } , \frac { 7 } { 5 }$

Question 34

For the given general term an, write an expression using $\Sigma$ to represent the indicated p to represent the indicated partial sum.

- $a _ { n } = 2 - 6 n,$ third partial sum

A) $\sum _ { i = 1 } ^ { n } 2 - 6 i$
B) $\sum _ { i = 1 } ^ { 3 } 2 - 6 i$
C) $\sum _ { i = 0 } ^ { 2 } 2 - 6 i$
D) $\sum _ { i = 0 } ^ { 3 } 2 - 6 i$

Question 35

Evalutate the series.

- $$\sum _ { n = 3 } ^ { 5 } \left( n ^ { 2 } - 4 \right)$$

A)35
B)38
C)0
D)12

Question 36

Find the first and third partial sums, s1 and s3, for the sequence

- $$a _ { n } = \frac { n } { n + 2 }$$

A) $\frac { 1 } { 3 } , \frac { 43 } { 30 }$
B) $\frac { 1 } { 3 } , \frac { 1 } { 10 }$
C) $\frac { 1 } { 3 } , \frac { 3 } { 4 }$
D) $\frac { 1 } { 3 } , \frac { 3 } { 5 }$

Question 37

For the set of valueses $x _ { 1 } = 1 , x _ { 2 } = 3 , x _ { 3 } = - 2,$ 2, a nd x4 = 6, find the following.

- $\sum _ { i = 1 } ^ { 4 } 5 x _ { i }$

A)41
B)8
C)40
D)35

Question 38

For the given general term an, write an expression using $\Sigma$ to represent the indicated p to represent the indicated partial sum.

- $a _ { n } = \frac { n } { n - 9 },$ third partial sum

A) $\sum _ { i = 1 } ^ { 3 } \frac { i } { i - 9 }$
B) $\sum _ { i = 1 } ^ { n } \frac { i } { i - 9 }$
C) $\sum _ { i = 0 } ^ { 3 } \frac { i } { i - 9 }$
D) $\sum _ { i = 0 } ^ { 2 } \frac { i } { i - 9 }$

Question 39

Find the first and third partial sums, s1 and s3, for the sequence

- $$a _ { n } = 3 n + 9$$

A)12, 45
B)12, 18
C)12, 36
D)12, 42

Question 40

For the given general term an, write an expression using $\Sigma$ to represent the indicated p to represent the indicated partial sum.

- $a _ { n } = 8 n,$ fourth partial sum

A) $\sum _ { i = 5 } ^ { 5 } 8 i$
B) $\sum _ { i = 1 } ^ { 5 } 8 i$
C) $\sum _ { i = 1 } ^ { 4 } 8 i$
D) $\sum _ { i = 0 } ^ { 4 } 8 i$

Question 41

Find the common difference of the sequence.

- $\mathrm { a } _ { 1 } = 814 , \mathrm { a } _ { 4 } = 829 \text {; find } \mathrm { d }$

A)-814
B)814
C)-5
D)5

Question 42

Find the common difference of the sequence.

- $a _ { 1 } = - 12 , a _ { 4 } = - 24 ; \text { find } d$

A)-8
B)-4
C)-12
D)12

Question 43

Find the indicated quantity of the arithmetic sequence.

- $a _ { 1 } = 25 , a _ { n } = - 631 , d = - 16 ; \text { find } n$

A)41
B)10
C)42
D)58

Question 44

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence.

- $a _ { 1 } = 1 , d = 3$

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

Question 45

Find the indicated quantity of the arithmetic sequence.

-a1 = -5, d = -8; find $\mathrm { a } _ { 5 }$

A)27
B)-37
C)-45
D)37

Question 46

Find the indicated quantity of the arithmetic sequence.

-a1 = 7 , d = 1 ; find $\mathrm { a } _ { 13 }$

A)- 6
B)- 5
C)20
D)19

Question 47

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence.

- $a _ { 1 } = - 12 , d = - 4$

A) $a _ { n } = - 4 n - 12$
B) $a _ { n } = 4 n + 8$
C) $a _ { n } = 4 n + 12$
D) $a _ { n } = - 4 n - 8$

Question 48

Find the common difference of the sequence.

- $\mathrm { a } _ { 1 } = 3.82 , \mathrm { a } _ { 4 } = 12.16 ; \text { find } \mathrm { d }$

A)8.34
B)2.78
C)3.82
D)2.085

Question 49

Write the first five terms of the arithmetic sequence with the given term and common difference.

-a $a _ { 1 } = 10 , d = 4$

A)10, 13, 16, 19, 22
B)14, 18, 22, 26, 30
C)0, 10, 14, 18, 22
D)10, 14, 18, 22, 26

Question 50

Find the indicated quantity of the arithmetic sequence.

- $a _ { 1 } = 6 , a _ { n } = - 74 , d = - 4 ; \text { find } n$

A)21
B)22
C)20
D)17

Question 51

Write the first five terms of the arithmetic sequence with the given term and common difference.

- $a _ { 1 } = - 24 , d = 6$

A)-24, -18, -12, -6, 0
B)0, -6, -12, -18, -24
C)-12, -18, -24, -30, -36
D)-12, -6, 0, 6, 12

Question 52

Find the indicated quantity of the arithmetic sequence.

-a1 = -19, d = -3; find $\mathrm { a } _ { 120 }$ 120

A)-376
B)338
C)-379
D)341

Question 53

Find the common difference of the sequence.

- $a _ { 1 } = \frac { 9 } { 2 } , a _ { 4 } = \frac { 21 } { 2 } ; \text { find } \mathrm { d }$

A)2
B) $\frac { 1 } { 2 }$
C)4
D)6

Question 54

Find the common difference of the sequence.

- $$a _ { 1 } = 6 , a _ { 4 } = 18 \text {; find } d$$

A)-4
B)-12
C)12
D)4

Question 55

Write the first five terms of the arithmetic sequence with the given term and common difference.

- $a _ { 1 } = 9 , d = - 3$

A)9, 6, 3, 0, -3
B)12, 9, 6, 3, 0
C)9, 6, 2, 0, -3
D)6, 3, 0, -3, -6

Question 56

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence.

- $a _ { 1 } = 2 , d = 8$

A) $a _ { n } = 8 n - 6$
B) $a _ { n } = 6 n - 3$
C) $a _ { n } = 6 n - 8$
D) $a _ { n } = 8 n - 3$

Question 57

Write the first five terms of the arithmetic sequence with the given term and common difference.

- $a _ { 1 } = \frac { 3 } { 8 } , d = - \frac { 1 } { 8 }$

A) $\frac { 3 } { 8 } , \frac { 1 } { 4 } , \frac { 5 } { 8 } , 0 , \frac { 7 } { 8 }$
B) $\frac { 3 } { 8 } , \frac { 1 } { 2 } , \frac { 5 } { 8 } , \frac { 3 } { 4 } , \frac { 7 } { 8 }$
C) $\frac { 3 } { 8 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , 0 , - \frac { 1 } { 8 }$
D) $\frac { 3 } { 8 } , \frac { 3 } { 4 } , \frac { 9 } { 8 } , \frac { 3 } { 2 } , \frac { 15 } { 8 }$

Question 58

Find the indicated quantity of the arithmetic sequence.

-a1 = -6 , d = 1 ; find $\mathrm { a } _ { 40 }$

A)34
B)33
C)-45
D)-46

Question 59

Find the indicated quantity of the arithmetic sequence.

-a1 = 5 , d = -3 ; find $a _ { 8 }$

A)26
B)-16
C)29
D)-19

Question 60

Write the first five terms of the arithmetic sequence with the given term and common difference.

- $\mathrm { a } _ { 1 } = 1.4 , \mathrm {~d} = 0.7$

A) $2.1,2.8,3.5,4.2,4.9$
B) $1.4,0.7,0 , - 0.7 , - 1.4$
C) $0.7,0 , - 0.7 , - 1.4 , - 2.1$
D) $1.4,2.1,2.8,3.5,4.2$

Question 61

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.

-2, 4, 6, 8, . . ., 110

A)3135
B)3088
C)3080
D)112

Question 62

Solve the problem.
A grocery store display of apples has a total of 16 rows. The bottom row requires 103 apples. Each successive row requires 5 less apples than the prior one. How many apples are required to build the display?

A)1048 apples
B)2248 apples
C)1008 apples
D)2096 apples

Question 63

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.

-Find the sum of the first 90 positive even integers.

A)8190
B)8095
C)8194
D)8099

Question 64

Write the expression for the general (or nth)term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.

- $a = 2 , d = 7 ; \text { find } a _ { n } \text { and } a_{ 16}$

A) $a _ { n } = 2 + 7 n , a _ { 16 } = 107$
B) $a _ { n } = - 5 - 7 n , a _ { 16 } = 107$
C) $a _ { n } = - 5 + 7 n , a _ { 16 } = 37$
D) $a _ { n } = - 5 + 7 n , a _ { 16 } = 107$

Question 65

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.

- $a _ { 1 } = - 8 , d = - 12 ; \text { find } s _ { 6 }$

A)228
B)-120
C)- 228
D)-60

Question 66

Solve the problem.
A school auditorium has 34 rows with 21 seats in the first row, 24 in the second row, 27 in the third row, and so forth. How many seats are in the auditorium?

A)2448 seats
B)4896 seats
C)2397 seats
D)4794 seats

Question 67

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence.

- $a _ { 1 } = \frac { 6 } { 5 } , d = - \frac { 1 } { 5 }$

A) $a _ { n } = - \frac { 1 } { 5 } n + \frac { 6 } { 5 }$
B) $$a _ { n } = \frac { 6 } { 5 } n - \frac { 7 } { 5 }$$
C) $$a _ { n } = - \frac { 1 } { 5 } n + \frac { 7 } { 5 }$$
D) $a _ { n } = \frac { 6 } { 5 } n - \frac { 1 } { 5 }$

Question 68

Write the expression for the general (or nth)term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.

- $a = 5 , d = - 5 ; \quad \text { find } a _ { n } \text { and } a _ { 15 }$

A) $a _ { n } = 10 + 5 n , a _ { 15 } = - 65$
B) $a _ { n } = 10 - 5 n , a _ { 15 } = - 65$
C) $a _ { n } = 10 - 5 n , a _ { 15 } = - 25$
D) $a _ { n } = 5 - 5 n , a _ { 15 } = - 65$

Question 69

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.

-15, 6, -3, -12, . . ., -156

A)-165
B)-1410
C)-1500
D)-1404

Question 70

For the geometric sequence, find the common ratio, r.

-2, 6, 18, 54, 162, . . .

A)18
B)3
C) $\frac { 1 } { 3 }$
D)6

Question 71

Write the expression for the general (or nth)term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.

- $a = 97 , d = - 9 ; \quad \text { find } a _ { n } \text { and} a_8$

A) $a _ { n } = 106 - 9 n , a _ { 8 } = - 11$
B) $a _ { n } = 97 - 9 n , a _ { 8 } = 34$
C) $a _ { n } = 97 - 9 n , a _ { 8 } = - 11$
D) $a _ { n } = 106 - 9 n , a _ { 8 } = 34$

Question 72

Write the expression for the general (or nth)term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.

- $a = - 10 , d = 3 ; \quad \text { find } a _ { n } \text { and } a _ { 7 }$

A) $a _ { n } = - 13 - 3 n , a _ { 7 } = 8$
B) $a _ { n } = - 13 + 3 n , a _ { 7 } = 8$
C) $a _ { n } = - 10 + 3 n , a _ { 7 } = 8$
D) $a _ { n } = - 13 + 3 n , a _ { 7 } = 32$

Question 73

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.

- $a _ { 1 } = 8 , d = 10 ; \text { find } \mathrm { s } _ { 5 }$

A)90
B)140
C)280
D)54

Question 74

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.

-8, 14, 20, 26, . . ., 242

A)5010
B)5000
C)248
D)5120

Question 75

For the geometric sequence, find the common ratio, r.
4, -12, 36, -108, 324, . . .

A)-16
B)-3
C)36
D)3

Question 76

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.

- $a _ { 1 } = 5 , d = 4 ; \text { find } s 60$

A)7500
B)7257
C)7380
D)6875

Question 77

Solve the problem.
Deborah is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $110 during her first year on the job. Find her monthly salary at the end of her first year.

A)$4100
B)$3110
C)$4210
D)$4320

Question 78

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.

-Find the sum of the odd integers between 18 and 54.

A)684
B)720
C)648
D)612

Question 79

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.

--13, -23, -33, -43, . . ., -703

A)-25,410
B)-713
C)-25,060
D)-25,051

Question 80

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence.

- $a _ { 1 } = - 2 , d = 0.2$

A) $a _ { n } = - 2 n + 2.2$
B) $a _ { n } = 0.2 n - 2$
C) $a _ { n } = 0.2 n - 2.2$
D) $a _ { n } = - 2 n + 0.2$