Apps. and Interpretation for IBDP Maths Ebook 1 | Page 77

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Paper 2 – Arithmetic and Geometric Sequences
Example
Consider an arithmetic sequence u1, u2, u3, , u , where u1 � 264 , u2 � 276 and
u3 � 288 .
n
(a) Find the value of u
17
.
[2]
(b) Find the sum of the first 23 terms of the sequence.
[3]
40 40 40
Now consider the sequence v1 , v2, v3, , v
n,
where v1
� , v2
� and v3
� .
729 243 81
This sequence continues in the same manner.
(c) Find the value of v
13
.
[2]
(d) Find the sum of the first 13 terms of this sequence, giving the answer correct to
the nearest integer.
[3]
Let k be a positive integer such that uk
� v .
k
8
(e) Calculate the value of k .
[3]
Solution
(a) u
17
(b)
� u1 � (17 � 1) d
(M1) for valid approach
� 264 � (17 � 1)(12)
� 456
A1 N2
The sum of the first 23 terms
� 23 � u (23 1)
1
� � d�
2
(M1) for valid approach
� 23 � � (23 � 1)(12) �
2
(A1) for substitution
� 9108
A1 N2
[2]
[3]
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