| Date | May 2014 | Marks available | 3 | 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 \(d\) (M1)
eg \(\frac{{16 - 10}}{2}{\text{, }}10 - 2d = 16 - 4d{\text{, }}2d = 6{\text{, }}d = 6\)
\(d = 3\) A1 N2
[2 marks]
a.
correct approach (A1)
eg \(10 = {u_1} + 2 \times 3{\text{, }}10 - 3 - 3\)
\({u_1} = 4\) A1 N2
[2 marks]
b.
correct substitution into sum or term formula (A1)
eg \(\frac{{20}}{2}(2 \times 4 + 19 \times 3){\text{, }}{u_{20}} = 4 + 19 \times 3\)
correct simplification (A1)
eg \(8 + 57{\text{, }}4 + 61\)
\({S_{20}} = 650\) 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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