Sequences and series Flashcards
Sequence definition
A list of numbers, set out in a particular order such that each number can be calculated from the one before.
Term
Each number in a sequence
3,7,11,15,19….. type of sequence and nth term formula
Infinite sequence and Un=4n-1
6,11,16,21….,51 type of sequence and nth term formula
Finite sequence and Un = 5n+1
Arithmetic sequence definition
A sequence where each term differs to the one before by adding or subtracting a constant.
General nth term formula for arithmetic sequence
Un =a+(n-1)d
Where Un is the nth term
a is starting value, n is number of value being found and d is difference between terms.
Series definition
Sum of all terms in a sequence
Sum of n terms denotation
Sn
Formula for Sn for arithmetic sequences
Sn =1/2*n(2a+(n-1)d)
Where Sn is sum of n terms
n is number of terms
a is first term
d is difference between terms
Geometric sequence definition
A sequence where the next term is found by multiplying the previous term by a constant number
nth term formula for geometric series
Un=ar^(n-1)
Where Un is nth term
a is first term
r is ratio between terms (multiplier)
n is number of terms.
Sum of n terms of a geometric series formula
Sn=a(1-r^n)/1-r
Sn is sum of n terms
a is first term
r is ratio between terms(multiplier)
n is number of terms.
When can the sum to infinity of a geometric series be calculated ?
|r|<1, magnitude of r is less than 1
Sum to infinity equation
S ∞ =a/1-r
S ∞ is sum to infinity
a is first term
r is ratio between terms where |r| < 1
How to work out r in geometric series for terms between one another
r=un/un-1
