Number Sequences
Number sequences is a topic where students are given a pattern of numbers and asked to either find the next few terms or determine the general term (a formula for the pattern).
The most challenging part for many students is finding the general term, as it requires students to study how the sequence changes.
In general, there are three main types of sequences you need to know: linear sequences, quadratic sequences, and cubic sequences. In addition, some special patterns include perfect square sequences and perfect cube sequences. In this course, you will learn how to identify these patterns and determine its general term.
Related Lessons:
Linear Sequence
Linear sequences are the most commonly tested type of sequence in exams, so it is important for students to understand how to identify the common difference and form the general term quickly and accurately.
A linear sequence is a type of number pattern where the terms increase or decrease by the same amount each time. This means there is a constant difference between consecutive terms.
The general formula for a linear sequence is:
\(T_n = an + b\)
Quadratic Sequence
Quadratic sequences are also commonly tested in exams, especially in questions that require students to find the general term.
The general formula for a quadratic sequence is:
\(T_n = an^2 + bn + c\)
A quadratic sequence is a type of number pattern where the differences between terms are not constant, but the second differences are constant.
Cubic Sequence
Cubic sequences are less common than linear and quadratic sequences but may still appear in exams.
A cubic sequence is a type of number pattern where the first and second differences are not constant, but the third differences are constant. This means you need to find the differences between terms three times before you get a constant value.
The general formula for a cubic sequence is:
\(T_n = an^3 + bn^2 + cn + d\)
Perfect Square Sequence
Perfect square sequences are important because they often appear as part of more complex patterns. Students should learn to recognise square numbers quickly.
A perfect square sequence is a number pattern where each term is a square number, meaning it is the result of multiplying a number by itself.
The general form of a perfect square sequence is:
\(T_n = n^2\)
This gives a sequence like 1, 4, 9, 16, 25, and so on. Perfect square sequence is a subset of the quadratic sequence.
Perfect Cube Sequence
A perfect cube sequence is a number pattern where each term is a cube number, meaning it is the result of multiplying a number by itself twice (number × number × number).
The general form of a perfect cube sequence is:
\(T_n = n^3\)
This gives a sequence like 1, 8, 27, 64, 125, and so on. Perfect cube sequence is a subset of the cubic sequence.