| Date | May 2017 | Marks available | 4 | Reference code | 17M.1.hl.TZ1.7 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 7 | Adapted from | N/A |
Question
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]
a.
determine the value of \(\sum\limits_{r = 1}^N {{u_r}} \).
[3]
b.
Markscheme
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]
a.
\(1 + (N - 1) \times - 2 = - 15\)
\(N = 9\) (A1)
\(\sum\limits_{r = 1}^9 {{u_r}} = \frac{9}{2}(2 + 8 \times - 2)\) (M1)
\( = - 63\) A1
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
