Your Practice Paper – Analysis and Approaches HL for IBDP Mathematics

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 )

Binomial Theorem

� Properties of the n factorial n !:

1 . n! � n�( n �1 ) �( n � 2 ) � �3�2�

1

2 . 0 ! � 1 3 . n! � n�( n � 1 )!

8

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