| Date | May 2014 | Marks available | 4 | Reference code | 14M.1.sl.TZ2.7 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 7 | Adapted from | N/A |
Question
The sums of the terms of a sequence follow the pattern
S1=1+k, S2=5+3k, S3=12+7k, S4=22+15k, …, where k∈Z.
Given that u1=1+k, find u2, u3 and u4.
[4]
a.
Find a general expression for un.
[4]
b.
Markscheme
valid method (M1)
eg u2=S2−S1, 1+k+u2=5+3k
u2=4+2k, u3=7+4k, u4=10+8k A1A1A1 N4
[4 marks]
a.
correct AP or GP (A1)
eg finding common difference is 3, common ratio is 2
valid approach using arithmetic and geometric formulas (M1)
eg 1+3(n−1) and rn−1k
un=3n−2+2n−1k A1A1 N4
Note: Award A1 for 3n−2, A1 for 2n−1k.
[4 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 1 - Algebra » 1.1 » Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.
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