Intermediate Algebra

Lynn Marecek

Chapter 12

Sequences, Series and Binomial Theorem - all with Video Answers

Educators

Section 1

Sequences

Problem 1

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=2 n-7$

Monica Miller

Monica Miller

Numerade Educator

Problem 2

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=5 n-1$

Monica Miller

Numerade Educator

Problem 3

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=3 n+1$

Monica Miller

Numerade Educator

Problem 4

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=4 n+2$

Monica Miller

Numerade Educator

Problem 5

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=2^n+3$

Monica Miller

Numerade Educator

Problem 6

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=3^n-1$

Monica Miller

Numerade Educator

Problem 7

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=3^n-2 n$

Angela Guo

Numerade Educator

Problem 8

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=2^n-3 n$

Monica Miller

Numerade Educator

Problem 9

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=\frac{2^n}{n^2}$

Monica Miller

Numerade Educator

Problem 10

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=\frac{3^n}{n^3}$

Monica Miller

Numerade Educator

Problem 11

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=\frac{4 n-2}{2^n}$

Monica Miller

Numerade Educator

Problem 12

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=\frac{3 n+3}{3^n}$

Monica Miller

Numerade Educator

Problem 13

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=(-1)^n \cdot 2 n$

Rakesh Kumar Sharma

Rakesh Kumar Sharma

Numerade Educator

Problem 14

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=(-1)^n \cdot 3 n$

Monica Miller

Numerade Educator

Problem 15

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=(-1)^{n+1} n^2$

Monica Miller

Numerade Educator

Problem 16

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=(-1)^{n+1} n^4$

Monica Miller

Numerade Educator

Problem 17

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=\frac{(-1)^{n+1}}{n^2}$

Monica Miller

Numerade Educator

Problem 18

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_n=\frac{(-1)^{n+1}}{2 n}$

Monica Miller

Numerade Educator

Problem 19

In the following exercises, find a general term for the sequence whose first five terms are shown.
$8,16,24,32,40, \ldots$

Monica Miller

Numerade Educator

Problem 20

In the following exercises, find a general term for the sequence whose first five terms are shown.
$7,14,21,28,35, \ldots$

Monica Miller

Numerade Educator

Problem 21

In the following exercises, find a general term for the sequence whose first five terms are shown.
$6,7,8,9,10, \ldots$

Monica Miller

Numerade Educator

Problem 22

In the following exercises, find a general term for the sequence whose first five terms are shown.
$-3,-2,-1,0,1, \ldots$

Monica Miller

Numerade Educator

Problem 23

In the following exercises, find a general term for the sequence whose first five terms are shown.
$e^3, e^4, e^5, e^6, e^7, \ldots$

Monica Miller

Numerade Educator

Problem 24

In the following exercises, find a general term for the sequence whose first five terms are shown.
$\frac{1}{e^2}, \frac{1}{e}, 1, e, e^2, \ldots$

Monica Miller

Numerade Educator

Problem 25

In the following exercises, find a general term for the sequence whose first five terms are shown.
$-5,10,-15,20,-25, \ldots$

Monica Miller

Numerade Educator

Problem 26

In the following exercises, find a general term for the sequence whose first five terms are shown.
$-6,11,-16,21,-26, \ldots$

Monica Miller

Numerade Educator

Problem 27

In the following exercises, find a general term for the sequence whose first five terms are shown.
$-1,8,-27,64,-125, \ldots$

Monica Miller

Numerade Educator

Problem 28

In the following exercises, find a general term for the sequence whose first five terms are shown.
$2,-5,10,-17,26, \ldots$

Monica Miller

Numerade Educator

Problem 29

In the following exercises, find a general term for the sequence whose first five terms are shown.
$-2,4,-6,8,-10, \ldots$

Monica Miller

Numerade Educator

Problem 30

In the following exercises, find a general term for the sequence whose first five terms are shown.
$1,-3,5,-7,9, \ldots$

Monica Miller

Numerade Educator

Problem 31

In the following exercises, find a general term for the sequence whose first five terms are shown.
$\frac{1}{4}, \frac{1}{16}, \frac{1}{64}, \frac{1}{256}, \frac{1}{1,024}, \ldots$

Monica Miller

Numerade Educator

Problem 32

In the following exercises, find a general term for the sequence whose first five terms are shown.
$\frac{1}{1}, \frac{1}{8}, \frac{1}{27}, \frac{1}{64}, \frac{1}{125}, \ldots$

Monica Miller

Numerade Educator

Problem 33

In the following exercises, find a general term for the sequence whose first five terms are shown.
$-\frac{1}{2},-\frac{2}{3},-\frac{3}{4},-\frac{4}{5},-\frac{5}{6}, \ldots$

Monica Miller

Numerade Educator

Problem 34

In the following exercises, find a general term for the sequence whose first five terms are shown.
$-2,-\frac{3}{2},-\frac{4}{3},-\frac{5}{4},-\frac{6}{5}, \ldots$

Monica Miller

Numerade Educator

Problem 35

In the following exercises, find a general term for the sequence whose first five terms are shown.
$-\frac{5}{2},-\frac{5}{4},-\frac{5}{8},-\frac{5}{16},-\frac{5}{32}, \ldots$

Monica Miller

Numerade Educator

Problem 36

In the following exercises, find a general term for the sequence whose first five terms are shown.
$4, \frac{1}{2}, \frac{4}{27}, \frac{4}{64}, \frac{4}{125}, \ldots$

Monica Miller

Numerade Educator

Problem 37

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=\frac{4}{n!}$

Monica Miller

Numerade Educator

Problem 38

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=\frac{5}{n!}$

Monica Miller

Numerade Educator

Problem 39

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=3 n$ !

Monica Miller

Numerade Educator

Problem 40

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=2 n$ !

Monica Miller

Numerade Educator

Problem 41

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=(2 n)!$

Monica Miller

Numerade Educator

Problem 42

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=(3 n)!$

Monica Miller

Numerade Educator

Problem 43

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=\frac{(n-1)!}{(n)!}$

Monica Miller

Numerade Educator

Problem 44

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=\frac{n!}{(n+1)!}$

Monica Miller

Numerade Educator

Problem 45

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=\frac{n!}{n^2}$

Monica Miller

Numerade Educator

Problem 46

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=\frac{n^2}{n!}$

Monica Miller

Numerade Educator

Problem 47

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=\frac{(n+1)!}{n^2}$

Monica Miller

Numerade Educator

Problem 48

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_n=\frac{(n+1)!}{2 n}$

Monica Miller

Numerade Educator

Problem 49

In the following exercises, expand the partial sum and find its value.
$\sum_{i=1}^5 i^2$

Monica Miller

Numerade Educator

Problem 50

In the following exercises, expand the partial sum and find its value.
$\sum_{i=1}^5 i^3$

Monica Miller

Numerade Educator

Problem 51

In the following exercises, expand the partial sum and find its value.
$\sum_{i=1}^6(2 i+3)$

Monica Miller

Numerade Educator

Problem 52

In the following exercises, expand the partial sum and find its value.
$\sum_{i=1}^6(3 i-2)$

Monica Miller

Numerade Educator

Problem 53

In the following exercises, expand the partial sum and find its value.
$\sum_{i=1}^4 2^i$

Monica Miller

Numerade Educator

Problem 54

In the following exercises, expand the partial sum and find its value.
$\sum_{i=1}^4 3^i$

Monica Miller

Numerade Educator

Problem 55

In the following exercises, expand the partial sum and find its value.
$\sum_{k=0}^3 \frac{4}{k!}$

Monica Miller

Numerade Educator

Problem 56

In the following exercises, expand the partial sum and find its value.
$\sum_{k=0}^4-\frac{1}{k!}$

Monica Miller

Numerade Educator

Problem 57

In the following exercises, expand the partial sum and find its value.
$\sum_{k=1} k(k+1)$

Monica Miller

Numerade Educator

Problem 58

In the following exercises, expand the partial sum and find its value.
$\sum_{k=1}^5 k(2 k-3)$

Monica Miller

Numerade Educator

Problem 59

In the following exercises, expand the partial sum and find its value.
$\sum_{n=1}^5 \frac{n}{n+1}$

Monica Miller

Numerade Educator

Problem 60

In the following exercises, expand the partial sum and find its value.
$\sum_{n=1}^4 \frac{n}{n+2}$

Monica Miller

Numerade Educator

Problem 61

In the following exercises, write each sum using summation notation.
$\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}$

Monica Miller

Numerade Educator

Problem 62

In the following exercises, write each sum using summation notation.
$\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\frac{1}{256}$

Monica Miller

Numerade Educator

Problem 63

In the following exercises, write each sum using summation notation.
$1+\frac{1}{8}+\frac{1}{27}+\frac{1}{64}+\frac{1}{125}$

Monica Miller

Numerade Educator

Problem 64

In the following exercises, write each sum using summation notation.
$\frac{1}{5}+\frac{1}{25}+\frac{1}{125}+\frac{1}{625}$

Monica Miller

Numerade Educator

Problem 65

In the following exercises, write each sum using summation notation.
$2+1+\frac{2}{3}+\frac{1}{2}+\frac{2}{5}$

Monica Miller

Numerade Educator

Problem 66

In the following exercises, write each sum using summation notation.
$3+\frac{3}{2}+1+\frac{3}{4}+\frac{3}{5}+\frac{1}{2}$

Monica Miller

Numerade Educator

Problem 67

In the following exercises, write each sum using summation notation.
$3-6+9-12+15$

Monica Miller

Numerade Educator

Problem 68

In the following exercises, write each sum using summation notation.
$-5+10-15+20-25$

Monica Miller

Numerade Educator

Problem 69

In the following exercises, write each sum using summation notation.
$-2+4-6+8-10+\ldots+20$

Monica Miller

Numerade Educator

Problem 70

In the following exercises, write each sum using summation notation.
$1-3+5-7+9+\ldots+21$

Monica Miller

Numerade Educator

Problem 71

In the following exercises, write each sum using summation notation.
$14+16+18+20+22+24+26$

Monica Miller

Numerade Educator

Problem 72

In the following exercises, write each sum using summation notation.
$9+11+13+15+17+19+21$

Monica Miller

Numerade Educator

Problem 73

In your own words, explain how to write the terms of a sequence when you know the formula. Show an example to illustrate your explanation.

Nicole Hoffman

Numerade Educator

Problem 74

Which terms of the sequence are negative when the $n^{\text {th }}$ term of the sequence is $a_n=(-1)^n(n+2)$ ?

Monica Miller

Numerade Educator

Problem 75

In your own words, explain what is meant by $n$ ! Show some examples to illustrate your explanation.

Joanna Quigley

Numerade Educator

Problem 76

Explain what each part of the notation $\sum_{k=1}^{12} 2 k$ means.

Monica Miller

Numerade Educator