Chapter Sections 11.1-11.3 Flashcards
What is a sequence?
A function with domain being the set of positive integers n=1,2,3,…
What is the general nth term formula?
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
If a pattern is like this: 2, -1, 2/3, -1/2, 2/5…. what do you automatically know?
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
What is this factorial?
0!
1
what is 1!
1
What is n!
n(n-1)!
What does a recursive formula mean?
it relies on the answer before or after
n+1 …. the next answer
n-1 …. the answer before
n-2 ….. two answers before
What would a recursive question look like?
it would give you an answer and then the formula…
ex) b1 = 1 b”sub”n= n*b”sub”(n-1)
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?
you put the first three answers and then do an equation with n in it as the last answer.
ex) 1, 2, 3,….n
When using your calculator what should you do when it asks you to give them the list of a summation notation
- 2nd + stat
- go to ops
- go to seq(
- fill in everything then paste
- THIS WILL GIVE YOU THE LIST
When using your calculator what should you do when it asks you to give them the sum a summation notation
- press math button
- go down to 0 which is summation
- fill in everything that is asked
- THIS WILL GIVE YOU THE SUM
what do you do when the summation notation is….. n over sigma and under sigma is k=1 and the “equation” is c
the answer would just be c*n
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
C * n over sigma, K=1 under the sigma and a”sub”k is the equation
what is the recursive formula?
a1=a1 a”sub”n = a”sub”n + d
what is d in the recursive formula?
the common difference
how do you calculate the common difference?
d= a”sub”n - a”sub”(n-1)
what is the nth term formula?
a”sub”n = a + (n-1)d
is a”sub”n = n^2 arithmetic?
no because the common difference is not the same
what is the equation for the sum of terms in arithmetic sequence
s”sub”n= (n/2) (a + a”sub”n)
how do you determine if something is arithmetic?
if when you figure out for d and the answer has a n in it then it is not arithmetic
What is the recursive formula for geometric sequences?
a1=a1 a”sub”n= r*a”sub”(n-1)
what is the nth term formula for geometric sequences?
a”sub”n= a*r^(n-1)
can r be 0?
no
what is r?
the ration between numbers in a geometric sequence
how do you find the sum of n terms of a geometric sequence?
s”sub”n= a * [(1-r^n)/(1-r)]
NOTE
-put parenthesis when needed
what does a mean?
first term
how do you find the sum of a geometric series with sigma?
infinity over the sigma, k=1 under the sigma, and the equation is a*r^k-1
if when finding the sum of a geometric series with sigma the absolute value of r is less than 1 then what happens?
the equation is just s”sub” infinity = a/ (1-r)
if the absolute value of r is less than 1 then what does this mean
it converges
