Sequences

Find two possible rules for the sequence: 1, 1, 1, 1, 1, 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

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:

Basic sequence definiton

A function whose domain is a countable totally ordered set.

A sequence in great analysis

A sequence is a function from a subset of the natural numbers to the real numbers.

Arithmetic Sequence Rule

Xn= x1 r n-1

Geometric sequence rule

Xn= x1 r n-1

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

Arithmetic Sqeuence

Has a constant difference between the terms

Geometric sequence basic definititon

Any sequence with is divided or multiplied by a constant

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