Analysis and Approaches for IBDP Maths Ebook 1 | Page 72

Your Practice Set – Analysis and Approaches for IBDP Mathematics
23
Paper 2 Section A – Finding ,
and
with given first three terms
Example
The first three terms of a geometric sequence are u1 � 1.024 , u2 � 1.28 and u3 � 1.6 .
(a) Find the value of r .
(b)
Find the value of
10
� un
.
n�1
(c) Find the least value of n such that Sn
� 2019 .
[2]
[2]
[3]
Solution
(a)
(b)
1.28
r � (M1) for finding r
1.024
r � 1.25
A1 N2
10
�
u
n
n�1
� S 10
10
1.024(1 �1.25 )
�
1�1.25
(A1) for substitution
� 34.05097266
� 34.1
A1 N2
(c) Sn
� 2019
n
1.024(1 �1.25 )
� 2019
1�1.25
n
�4.096(1 �1.25 ) � 2019
(M1) for correct formula
n
1�1.25 � � 492.9199219
1.25 n � 493.9199219
(A1) for setting an inequality
1.25 n �493.9199219 � 0
n
By considering the graph of y �1.25 � 493.9199219
n � 27.795441
�The least value of n is 28. A1 N1
[3]
[2]
[2]
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