Patterns and Sequences

1.3  Patterns and Sequences
  The pattern of a sequence is the rule or design of the sequence.  
Patterns of a sequences
(i)   Numbers
  \(3, 6, 9, 12, 15,...\)  

 Pattern: Addition of \(3\)

(ii)   Words 
  \(1, 9, 17, 25, 33, ...\)  

The sequence begins with the number \(1\) and the pattern is add \(8\) to the number before it.

(iii)   Algebraic expressions
  It is an expression which has a combination of basic mathematical operations on numbers, variables or other mathematical entities.  

It is written as \(3x\) where \(x=1,2,3,...\)

Terms of a sequence

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.

  \(\begin{aligned} &\space 65, 60, 55, 50, 45, 40, 35, 30,... \\\\& T_1, T_2, T_3, T_4, T_5, T_6, T_7, T_8, ... \end{aligned}\)  

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, \(T_8= 30\)