A sequence in great analysis
A sequence is a function from a subset of the natural numbers to the real numbers.
Basic sequence definiton
A function whose domain is a countable totally ordered set.
Arithmetic Sqeuence
Has a constant difference between the terms
Geometric Sequence Analytical Definition
A Geometric sequence is a mathematical sequence consisting of a sequence in which the next term originates by multiplying the predecessor with a constant, better known as the common ratio. When the first term x1 and the common ratio r are known, the whole sequence is fixed, or in formula:
Geometric sequence basic definititon
Any sequence with is divided or multiplied by a constant
Geometric sequence rule
Xn= x1 r n-1
Arithmetic Sequence Rule
Xn= x1 r n-1
Basic Arithmetic Sequence
1, 2, 3, 4, 5, 6
Basic Geometric Sequence (Increasing)
1, 2, 4, 8, 16, 32
Basic Geometric sequence (Decreasing)
32, 16, 8, 4, 2, 1
Find the common factor and ratio for this sequence 1, 2, 4, 8, 16, 32
The common factor is 2 and the common ratio 2/1 or just 2
Find the common factor and ratio for this sequence: 5, 25, 125, 625, 3125
The common factor is 5 and common ratio 5/1 or just 5
Find the constant difference of this sequence and it's rule: 6, 8, 10, 12, 14, 16
X∨n = 2N + 4 and the constant difference is 4
Find the constant difference for this sequence and a rule: 7, 14, 21, 28, 35, 42
X∨n = 7N and teh constant difference is 7
Find two possible rules for the sequence: 1, 1, 1, 1, 1, 1
...