18M.2.AHL.TZ1.H_1

pestleMathematicsAIHLPaper 218M· sl-1-2-arithmetic-sequences-and-seriessource ↗

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]

Calculate the number of positive terms in the sequence.

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

u₁ + 2d = 1407, u₁ + 9d = 1183 (M1)(A1)

u₁ = 1471, d = −32 A1A1

[4 marks]

1471 + (n − 1)(−32) > 0 (M1)

⇒ n < $\frac{{1471}}{{32}} + 1$

n < 46.96… (A1)

so 46 positive terms A1

[3 marks]

Examiners’ report

[N/A]