Arithmetic Sequences

Arithmetic Sequences - are sequences that add or subtract by a constant amount every step.

Examples of Arithmetic Sequences are shown below:

2, 4, 6, 8

5, 2, -1, -7

10, 20, 30, 40

Each of these sequences is adding/subtracting by the same amount every step. This common addition is called the Common Difference. We refer to the common difference as d. To find the common difference of an arithmetic sequence we can subtract the second value by the first value.

For example: the first sequence's difference is 4 - 2 = +2. The common difference for the 3 sequences above is shown below.

sequence 1 has a common difference of +2

sequence 2 has a common difference of -3

sequence 3 has a common difference of +10.

Try finding the common difference for each of these sequences:

-7, -3, 1, 5,

15, 10, 5, 0, -5

-100, 0, 100, 200

The position of an arithmetic sequence is represented by the letter n. The value of the sequences at position n is an.

The table above is a table of sequence 1 above. We can see that the common difference of the value is +2. The only difference is that this table displays the position of the value in the sequence. So, at position n = 1, we can see that the value of an, or the value in position 1 is 2. In position 2, the value of an is 4.

The last important piece of information is the starting value of the sequence. The starting point is referred to as a1. The starting point of the table above is where n = 1. The value of an is 2. So, the starting point of our arithmetic sequence is 2.

Try looking at the tables below and finding the common difference, d, and the starting value, a1.