Sequences and Series
Sequence - A set of numbers governed by a rule
Series - A sequence added together
Un = dn + c
n = term number, d = Common difference and c = movement
Series - A sequence added together
Un = dn + c
n = term number, d = Common difference and c = movement
Recurrence Relationships
Relationship between two or more terms compared to all other terms
E.g. Fibonacci Sequence
1,1,2,3,5,8 etc.
Un+2 = Un+1 + Un when U1 = 1, U2 = 1
E.g. Fibonacci Sequence
1,1,2,3,5,8 etc.
Un+2 = Un+1 + Un when U1 = 1, U2 = 1
Arithmetic Sequence/Series
In general:
1 2 3 4
a, (a+d), (a+2d), (a+3d)
Giving:
a + (n-1)d
a = First term n = term number d = common difference
1 2 3 4
a, (a+d), (a+2d), (a+3d)
Giving:
a + (n-1)d
a = First term n = term number d = common difference
Sum of Arithmetic Series
L = last number
Giving:
Sn = n (2a + (n-1)d)
2
or
Sn = n (a+L)
2
Remember the 2a in the brackets in the first equation
Giving:
Sn = n (2a + (n-1)d)
2
or
Sn = n (a+L)
2
Remember the 2a in the brackets in the first equation
Sigma Σ
Σ = Sum of
r = n
20 (Last term)
Σ 4r + 1 (rth term)
r=1 (First term)
This creates an arithmetic series so to find the sum use the Sn = n (a+l)
2
Σ 4r + 1 (rth term)
r=1 (First term)
This creates an arithmetic series so to find the sum use the Sn = n (a+l)
2