| Date | May 2018 | Marks available | 4 | Reference code | 18M.2.hl.TZ1.1 |
| Level | HL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
The 3rd term of an arithmetic sequence is 1407 and the 10th term is 1183.
Find the first term and the common difference of the sequence.
[4]
a.
Calculate the number of positive terms in the sequence.
[3]
b.
Markscheme
u1 + 2d = 1407, u1 + 9d = 1183 (M1)(A1)
u1 = 1471, d = −32 A1A1
[4 marks]
a.
1471 + (n − 1)(−32) > 0 (M1)
⇒ n < \(\frac{{1471}}{{32}} + 1\)
n < 46.96… (A1)
so 46 positive terms A1
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 1 - Core: 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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