Sequence and Series Flashcards
What is a sequence?
A Set of numbers in specific order determined by applying rule to nth term.
What is an infinite sequence?
A function whose domain is the set of all positive integers.
What is the special case factorial?
0!=1
What are the properties of sums in summation notation?
What are the formulas of summation notation?
What makes a sequence arithmetic?
If the difference between consecutive terms are the same.
What are the two equations for the nth of an arithmetic sequence
a(n)=a(1)+(n-1)d (most helpful)
a(n)=dn+c, where c=a(1)-d (basically the y-intercept)
What is the equation for a finite arithmetic sequence?
s(n)=(n/2)[a(1)+a(n)]
What is the nth partial sum?
The sum of the first n terms of an infinite sequence
If an equation in summation appears to be _____, it’s ____, therefore you should use the equation s(n)=(n/2)[a(1)+a(n)]
linear, arithmetic
If the lower limit is equal to 0, you should always ____ before determining the n number of terms.
Inspect the equation to see how plugging in n=0 will affect the summation.
How many terms (n)? 1) Lower limit = 0, upper limit = 10, equation = i^2
2) Lower limit = 0, upper limit = 5, equation = 300(1.06)^n
- n= 10
- n=6
What makes a sequence geometric?
The ratios of consecutive terms are the same (proceeding term/preceeding term = some recurring ratio)
What is the equation for nth term of a geometric sequence?
a(n)=(a1)(r)^n-1
What is the equation of a sum of a finite geometric sequence?
Sn=(a1)(1-r^n/1-r)
