| Date | May 2013 | Marks available | 2 | Reference code | 13M.1.sl.TZ1.12 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 12 | Adapted from | N/A |
Question
In an arithmetic sequence, the fifth term, u5, is greater than the first term, u1. The difference between these terms is 36.
Find the common difference, d.
The tenth term of the sequence is double the seventh term.
(i) Write down an equation in u1 and d to show this information.
(ii) Find u1.
Markscheme
\({u_1} + 4d - {u_1} = 36\) (M1)
Note: Accept equivalent forms including the use of a instead of \({u_1}\).
\((d =) 9\) (A1) (C2)
(i) \({u_{10}} = 2{u_7}\) (M1)
Note: Award (M1) for correct use of 2 (may be implied).
\({u_1} + 9d = 2[{u_1} + 6d]\) (A1)
Notes: Accept equivalent forms. Award (M1)(A0) for \(a + 9d = 2[a + 6d]\).
(ii) \({u_1} + 81 = 2{u_1} + 108\) (M1)
\(({u_1} =) - 27\) (A1)(ft) (C4)
Notes: Follow through from their d found in part (a) and equation in (b)(i). Do not penalize further use of a instead of \({u_1}\).
Examiners report
Some candidates confused geometric sequence with arithmetic sequence. Candidates found the algebraic manipulations difficult so scores on this question were weak.
Some candidates confused geometric sequence with arithmetic sequence. Candidates found the algebraic manipulations difficult so scores on this question were weak.
