Apps. and Interpretation for IBDP Maths Ebook 1 | Page 68

Your Practice Set – Applications and Interpretation for IBDP Mathematics
19
Paper 2 – Miscellaneous Problems
Example
In an arithmetic sequence, S30 � 5430 and u3 � 31. Let u
1
and d be the first term and the
common difference of the arithmetic sequence respectively.
(a) (i) Write down the first equation connecting u
1
and d .
(ii) Write down the second equation connecting u
1
and d .
(b)
(iii) Hence, write down the values of u
1
and d .
Find u
n
in terms of n .
(c) Find the smallest value of n such that un
� 888 .
(d)
Find S
n
in terms of n .
[6]
[2]
[3]
[2]
Solution
(a) (i) S30 � 5430
30 � 2 u (30 1) 1
� � d�
� 5430
(M1) for valid approach
2
30u
�435d
� 5430
A1 N2
1
(ii) u3 � 31
u1 � (3�1) d � 31
(M1) for valid approach
u1 �2d
� 31
A1 N2
(iii) u1 � 7
A1 N1
d � 12
A1 N1
(b) u � 7 � ( n� 1)(12)
(M1) for valid approach
n
un
�12n� 5
A1 N2
[6]
[2]
58
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