Arithmetic Sequences
Earlier, we learnt about number patterns, which included linear sequences with a common difference and quadratic sequences with a common second difference. We also looked at completing a sequence and how to determine the general term of a sequence.
In this section, we also look at geometric sequences, which have a constant ratio between consecutive terms. We will learn about arithmetic and geometric series, which are the summing of the terms in sequences.
Arithmetic Sequences
An arithmetic sequence is a sequence where consecutive terms are calculated by adding a constant value (positive or negative) to the previous term. We call this constant value the common difference (\(d\)).For example,\[\text{3}; \text{0}; -\text{3}; -\text{6}; -\text{9}; \ldots\]This is an arithmetic sequence because we add \(-\text{3}\) to each term to get the next term:
| First term | \(T_{1}\) | \(\text{3}\) | |
| Second term | \(T_{2}\) | \(3 + (-3) =\) | \(0\) |
| Third term | \(T_{3}\) | \(0 + (-3) =\) | \(-\text{3}\) |
| Fourth term | \(T_{4}\) | \(-3 + (-3) =\) | \(-\text{6}\) |
| Fifth term | \(T_{5}\) | \(-6 + (-3) =\) | \(-\text{9}\) |
| \(\vdots\) | \(\vdots\) | \(\vdots\) | \(\vdots\) |
Video:
This lesson is part of:
Sequences and Series