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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.

[2]
a.

Find the twelfth term.

[2]
b.

Find the sum of the first 100 terms.

[2]
c.

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]

a.

\(u_{12} = 7 + 11 \times 3\)     (M1)

\(= 40\)     (A1)(ft)     (C2)


Note: Accept list of numbers.

 

[2 marks]

b.

\(S_{100} = \frac{{100}}{{2}} (2 \times 7 + 99 \times 3)\)     (M1)


Note: Award (M1) for correct substitution in the AP formula.


= 15550     (A1)(ft)     (C2)


Note: Accept 15600

 

[2 marks]

c.

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.

a.

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.

b.

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.

c.

Syllabus sections

Topic 1 - Number and algebra » 1.7 » Arithmetic sequences and series, and their applications.
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