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Date May 2009 Marks available 3 Reference code 09M.2.sl.TZ1.1
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 1 Adapted from N/A

Question

In an arithmetic series, the first term is –7 and the sum of the first 20 terms is 620.

Find the common difference.

[3]
a.

Find the value of the 78th term.

[2]
b.

Markscheme

attempt to substitute into sum formula for AP (accept term formula)     (M1)

e.g. \({S_{20}} = \frac{{20}}{2}\left\{ {2( - 7) + 19\left. d \right\}} \right.\) , \(\left( {{\rm{or}}\frac{{20}}{2}\left( { - 7 + {u_{20}}} \right)} \right)\)

setting up correct equation using sum formula     A1

e.g. \(\frac{{20}}{2}\left\{ {2( - 7) + \left. {19d} \right\}} \right. = 620\)

\(d = 4\)     A1     N2

[3 marks]

a.

correct substitution \({u_{78}} = - 7 + 77(4)\)     (A1)

= 301     A1     N2

[2 marks]

b.

Examiners report

This question was generally well answered. Many candidates who got part (a) wrong, recovered and received full follow through marks in part (b). There were a few candidates who confused the term and sum formula in part (a).

a.

This question was generally well answered. Many candidates who got part (a) wrong, recovered and received full follow through marks in part (b). There were a few candidates who confused the term and sum formula in part (a).

b.

Syllabus sections

Topic 1 - Algebra » 1.1 » Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.
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