| Date | May 2014 | Marks available | 2 | Reference code | 14M.1.sl.TZ1.2 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
In an arithmetic sequence, the third term is 10 and the fifth term is 16.
Find the common difference.
[2]
a.
Find the first term.
[2]
b.
Find the sum of the first 20 terms of the sequence.
[3]
c.
Markscheme
attempt to find dd (M1)
eg 16−102, 10−2d=16−4d, 2d=6, d=616−102, 10−2d=16−4d, 2d=6, d=6
d=3d=3 A1 N2
[2 marks]
a.
correct approach (A1)
eg 10=u1+2×3, 10−3−310=u1+2×3, 10−3−3
u1=4u1=4 A1 N2
[2 marks]
b.
correct substitution into sum or term formula (A1)
eg 202(2×4+19×3), u20=4+19×3202(2×4+19×3), u20=4+19×3
correct simplification (A1)
eg 8+57, 4+618+57, 4+61
S20=650S20=650 A1 N2
[3 marks]
c.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.
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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