| Date | November 2009 | Marks available | 2 | Reference code | 09N.1.sl.TZ0.4 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
The first term of an arithmetic sequence is 7 and the sixth term is 22.
Find the common difference.
Find the twelfth term.
Find the sum of the first 100 terms.
Markscheme
\(7 + 5d = 22\) (M1)
Note: Award (M1) for correct substitution in the AP formula. Accept list of numbers as solution.
\(d = 3\) (A1) (C2)
[2 marks]
\(u_{12} = 7 + 11 \times 3\) (M1)
\(= 40\) (A1)(ft) (C2)
Note: Accept list of numbers.
[2 marks]
\(S_{100} = \frac{{100}}{{2}} (2 \times 7 + 99 \times 3)\) (M1)
Note: Award (M1) for correct substitution in the AP formula.
= 15550 (A1)(ft) (C2)
Note: Accept 15600
[2 marks]
Examiners report
Most candidates recognized the arithmetic sequence and used the correct formula, although some used a list to find the answers. A significant number of candidates were unable to find the sum of the first 100 terms and attempted to find the 100th term instead.
Most candidates recognized the arithmetic sequence and used the correct formula, although some used a list to find the answers. A significant number of candidates were unable to find the sum of the first 100 terms and attempted to find the 100th term instead.
Most candidates recognized the arithmetic sequence and used the correct formula, although some used a list to find the answers. A significant number of candidates were unable to find the sum of the first 100 terms and attempted to find the 100th term instead.
