Mathematics: Arithmetic Sequence

Home
Pattern Recognition
Simplifying Expressions
Sequences
Recursive Sequence
Arithmetic Sequence
Geometric Sequence
Trigonometry
Trigonometric Ratios
Periodic Function
Radian Measure
Trigonometric Identity

Hosted at teamapproach.ca

In an arithmetic sequence of numbers, the common difference is a constant.

For the general sequence a₁, a₂, a₃, ... , a_n, ... , the common difference d = a_n - a_n-1

The general term is   a_n = a₁ + (n-1)d   where a_n is the nth term and d is the common difference

Example arithmetic sequences are;

• 2, 4, 6, 8, 10, 12, ... , where d = 2
• 10, 5, 0 , -5, -10, -15, ... , where d = -5
• 0, 0.5, 1, 1.5, 2, 2.5, ... , where d = 0.5
• ¼, ½, ¾, 1, 1¼, 1½, ... , where d =  ¼

Because the common difference (rate of change) is constant, the relationship between n and a_n is linear.

Problem Example

if a₆ = 23 and a₁₁ = 38 then d = (38-23)/(11-6) = 15/5 = 3