Analysis and Approaches for IBDP Maths Ebook 1 | Page 77

25
Paper 1 Section A – Finding
with given a term in
Front Page
Example
In the expansion of (5x � 1) n , the coefficient of the term in x 2 is 87.5n , where n is a
positive integer. Find n .
Solution
[7]
(5x � 1) n
�(1 � 5 x) n
� n�
1 � n�
2
�1 � � �(5 x) � � �(5 x)
�
�1�
� 2�
(M1) for valid expansion
2 �n�
2
The term in x � � � (5 x)
�2�
(M1) for correct term
�n�
2
� �(5) � 87.5n
�2�
A1
nn ( �1) (25) � 87.5 n
2
(A1) for correct working
n �1 (25) � 87.5
2
(A1) for correct equation
(87.5)(2)
n �1
�
25
(A1) for simplification
n � 8
A1 N2
[7]
7
Exercise 25
1. In the expansion of (2x � 1) n , the coefficient of the term in x 2 is 540n , where n is a
positive integer. Find n .
[7]
2
2. In the expansion of (3x � 1) n , the coefficient of the term in x 2 is 18(2n � 1) , where n is a
positive integer. Find n .
[7]
n
3. In the expansion of (1 �x) (2 � nx)
, the coefficient of the term in x is 15. Find n .
[6]
n 2
4. In the expansion of (1 �x) (1 � nx)
, the coefficient of the term in x is � 99 , where n is a
positive integer. Find n .
[6]
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