## Patterns and Sequences

 1.3 Patterns and Sequences

 Definition The pattern of a sequence is the rule or design of the sequence.

Patterns of a sequences

(i)   Numbers

 Example $$3, 6, 9, 12, 15,...$$ Pattern: Addition of $$3$$

(ii)   Words

 Example $$1, 9, 17, 25, 33, ...$$ The sequence begins with the number $$1$$ and the pattern is add $$8$$ to the number before it.

(iii)   Algebraic expressions

 Definition It is an expression which has a combination of basic mathematical operations on numbers, variables or other mathematical entities.
 Example $$3,6,9,12,15,...$$ It is written as $$3x$$ where $$x=1,2,3,...$$

Terms of a sequence

 Definition The $$n^\text{th}$$ term is a number sequence and is written as $$T_n$$ whereby $$T$$ is the term and $$n$$ is the position of the term.

 Example \begin{aligned} &\space 65, 60, 55, 50, 45, 40, 35, 30,... \\\\& T_1, T_2, T_3, T_4, T_5, T_6, T_7, T_8, ... \end{aligned} First term, $$T_1= 65$$ Second term, $$T_2= -60$$ Third term, $$T_3= 55$$  Fourth term, $$T_4= 50$$ Fifth term, $$T_5= 45$$ Sixth term, $$T_6 = 40$$ Seventh term, $$T_7= 35$$ Eighth term, $$T_8= 30$$

## Patterns and Sequences

 1.3 Patterns and Sequences

 Definition The pattern of a sequence is the rule or design of the sequence.

Patterns of a sequences

(i)   Numbers

 Example $$3, 6, 9, 12, 15,...$$ Pattern: Addition of $$3$$

(ii)   Words

 Example $$1, 9, 17, 25, 33, ...$$ The sequence begins with the number $$1$$ and the pattern is add $$8$$ to the number before it.

(iii)   Algebraic expressions

 Definition It is an expression which has a combination of basic mathematical operations on numbers, variables or other mathematical entities.
 Example $$3,6,9,12,15,...$$ It is written as $$3x$$ where $$x=1,2,3,...$$

Terms of a sequence

 Definition The $$n^\text{th}$$ term is a number sequence and is written as $$T_n$$ whereby $$T$$ is the term and $$n$$ is the position of the term.

 Example \begin{aligned} &\space 65, 60, 55, 50, 45, 40, 35, 30,... \\\\& T_1, T_2, T_3, T_4, T_5, T_6, T_7, T_8, ... \end{aligned} First term, $$T_1= 65$$ Second term, $$T_2= -60$$ Third term, $$T_3= 55$$  Fourth term, $$T_4= 50$$ Fifth term, $$T_5= 45$$ Sixth term, $$T_6 = 40$$ Seventh term, $$T_7= 35$$ Eighth term, $$T_8= 30$$