Arithmetic Sequence with Examples

An arithmetic sequence is a series of numbers that has a common difference (d) between each consecutive term. This common difference can be found by subtracting any term from the next term in the sequence.

The general form of an arithmetic sequence is: {a, a+d, a+2d, a+3d, … } where a is the first term, and d is the common difference.

Example 1:
In the sequence 3, 8, 13, 18, 23, …, the common difference is 5 because: 8 – 3 = 5 13 – 8 = 5 18 – 13 = 5 and so on.

Example 2:

To find the 35th term in the sequence 3, 9, 15, 21, …: a_1 = 3 (the first term) d = 6 (the common difference, found by 9-3=6, 15-9=6, etc.) n = 35 (we want the 35th term)

Plugging into the formula: a_35 = 3 + 6(35-1) = 3 + 6(34) = 3 + 204 = 207

So the 35th term is 207.

Important things about arithmetic sequences:

The relationship between terms is always additive, not multiplicative. Look for a common difference between terms, not a common ratio.

A sequence with negative terms is not necessarily decreasing. It depends on the sign of the common difference. A positive common difference will produce an increasing sequence, even if the terms are negative.

Arithmetic Sequence Practice Questions