Chapter Sections 11.1-11.3

Question 1

What is a sequence?

Answer 1

A function with domain being the set of positive integers n=1,2,3,…

Question 2

What is the general nth term formula?

Answer 2

The formula to get the pattern in the sequence. For example, {An}= {1/2 ^n} is the general nth term formula for 1/2, 1/4, 1/8, 1/16, 1/32

Question 3

If a pattern is like this: 2, -1, 2/3, -1/2, 2/5…. what do you automatically know?

Answer 3

part of the general nth term formula is…
(-1)^n+1 if the pattern starts with a positive number

(-1)^n+2 if the pattern starts with a negative number

Question 4

What is this factorial?

0!

Answer 4

1

Question 5

what is 1!

Answer 5

1

Question 6

What is n!

Answer 6

n(n-1)!

Question 7

What does a recursive formula mean?

Answer 7

it relies on the answer before or after
n+1 …. the next answer
n-1 …. the answer before
n-2 ….. two answers before

Question 8

What would a recursive question look like?

Answer 8

it would give you an answer and then the formula…

ex) b1 = 1 b”sub”n= n*b”sub”(n-1)

Question 9

When given a summation notation with the sigma, K=1, and all that but the limit on top of sigma is n then what do you do when it asks you for the sum?

Answer 9

you put the first three answers and then do an equation with n in it as the last answer.
ex) 1, 2, 3,….n

Question 10

When using your calculator what should you do when it asks you to give them the list of a summation notation

Answer 10

• 2nd + stat
• go to ops
• go to seq(
• fill in everything then paste
• THIS WILL GIVE YOU THE LIST

Question 11

When using your calculator what should you do when it asks you to give them the sum a summation notation

Answer 11

• press math button
• go down to 0 which is summation
• fill in everything that is asked
• THIS WILL GIVE YOU THE SUM

Question 12

what do you do when the summation notation is….. n over sigma and under sigma is k=1 and the “equation” is c

Answer 12

the answer would just be c*n

Question 13

what is the same as the summation notation is….. n over sigma and under sigma is k=1 and the “equation” is c*a”sub”k

Answer 13

C * n over sigma, K=1 under the sigma and a”sub”k is the equation

Question 14

what is the recursive formula?

Answer 14

a1=a1 a”sub”n = a”sub”n + d

Question 15

what is d in the recursive formula?

Answer 15

the common difference

Question 16

how do you calculate the common difference?

Answer 16

d= a”sub”n - a”sub”(n-1)

Question 17

what is the nth term formula?

Answer 17

a”sub”n = a + (n-1)d

Question 18

is a”sub”n = n^2 arithmetic?

Answer 18

no because the common difference is not the same

Question 19

what is the equation for the sum of terms in arithmetic sequence

Answer 19

s”sub”n= (n/2) (a + a”sub”n)

Question 20

how do you determine if something is arithmetic?

Answer 20

if when you figure out for d and the answer has a n in it then it is not arithmetic

Question 21

What is the recursive formula for geometric sequences?

Answer 21

a1=a1 a”sub”n= r*a”sub”(n-1)

Question 22

what is the nth term formula for geometric sequences?

Answer 22

a”sub”n= a*r^(n-1)

Question 23

can r be 0?

Answer 23

no

Question 24

what is r?

Answer 24

the ration between numbers in a geometric sequence

Question 25

how do you find the sum of n terms of a geometric sequence?

Answer 25

s”sub”n= a * [(1-r^n)/(1-r)]

Question 26

NOTE

Answer 26

-put parenthesis when needed

Question 27

what does a mean?

Answer 27

first term

Question 28

how do you find the sum of a geometric series with sigma?

Answer 28

infinity over the sigma, k=1 under the sigma, and the equation is a*r^k-1

Question 29

if when finding the sum of a geometric series with sigma the absolute value of r is less than 1 then what happens?

Answer 29

the equation is just s”sub” infinity = a/ (1-r)

Question 30

if the absolute value of r is less than 1 then what does this mean

Answer 30

it converges