Mathematics · Oct / Nov 2021 · Paper 21 · Question 2
YMA01
As printed in the paper
The question as text
2. A sequence is defined by u1 = 6 un+1 = kun + 3 where k is a positive constant.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
2(a)[2]
Attempts to substitute
u
=
6
k
+
3
in
u
=
ku
+
2
3
2
(
)
u
=
k
6
k
+
3
+
3
3
3
∑
117
6
6
3
(6
3)
3
117
2(b)[3]
Uses
u
=
⇒
+
k
+ +
k
k
+
+
=
n
n
=
1
6
k
2
+
9
k
−
105
=
0
⇒
k
=
...
7
k =
2
(a)
3u . Allow if the “+3” is missing once only. E.g. score
M1: Attempts a full method of finding
for an attempt at substituting
u
=
6
k
+
3
into
u
=
ku
2 ( 3)
+
or their
u into
2
3
2
u
=
6
u
+
3
3
2
May be implied by a correct answer, but an incorrect answer with no substitution is M0.
(
)
2
A1:
u
=
k
6
k
+
3
+
3
OR
u
=
6
k
+
3
k
+
3
but isw after a correct answer is seen
3
3
(b)
M1: Sets their
u
+
u
+
u
=
117
to produce an equation in just k.
1
2
3
dM1: Solves a 3TQ by any valid method to find at least one value for k.
7
k =
A1:
ONLY
2
3
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