Arithmetic Sequences

� Properties of an arithmetic sequence u n

:

1 . u

1

: First term 2 . d � u2 �u1 � un

� un

_� 1: Common difference 3 . u � u1 � ( n � 1 ) d : General term ( n th term ) n n n

�

1� � �

1� : The sum of the first n n terms

2 2

4 . S �2 u ( n 1 ) d� �u u � n

: Summation sign

Geometric Sequences

� Properties of a geometric sequence u n

:

1 . u

1

: First term 2 . r � u2 �u1 � un

� un

_� 1

: Common ratio

3 . u u r ^�

n 1 n

�

1

� : General term ( n th term )

1

4 . ^{( 1} n

u � r S ⁾ n

� : The sum of the first n terms 1� r

Financial Mathematics

� Compound Interest :

PV : Present value r %: Interest rate per annum ( per year ) n : Number of years k : Number of compounded periods in one year kn

� r � FV �PV

�1�

� : Future value � ₁₀₀ k �

I �FV � PV : Interest

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