17M.1.AHL.TZ1.H_7

pestleMathematicsAAHLPaper 117M· sl-1-2-arithmetic-sequences-and-seriessource ↗

An arithmetic sequence ${u_1}{\text{, }}{u_2}{\text{, }}{u_3} \ldots$ has ${u_1} = 1$ and common difference $d \ne 0$ . Given that ${u_2}{\text{, }}{u_3}$ and ${u_6}$ are the first three terms of a geometric sequence

Given that ${u_N} = - 15$

find the value of $d$ .

[4]

determine the value of $\sum\limits_{r = 1}^N {{u_r}}$ .

[3]

Markscheme / solution

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

use of ${u_n} = {u_1} + (n - 1)d$ M1

${(1 + 2d)^2} = (1 + d)(1 + 5d)$ (or equivalent) M1A1

$d = - 2$ A1

[4 marks]

$1 + (N - 1) \times - 2 = - 15$

$N = 9$ (A1)

$\sum\limits_{r = 1}^9 {{u_r}} = \frac{9}{2}(2 + 8 \times - 2)$ (M1)

$= - 63$ A1

[3 marks]

Examiners’ report

[N/A]