18N.2.SL.TZ0.S_5

pestleMathematicsAISLPaper 218N· sl-1-2-arithmetic-sequences-and-seriessource ↗

The sum of an infinite geometric sequence is 33.25. The second term of the sequence is 7.98. Find the possible values of $r$ .

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

correct substitution into formula for infinite geometric series (A1)

eg $33.25 = \frac{{{u_1}}}{{1 - r}}$

correct substitution into formula for ${u_n}$ (seen anywhere) (A1)

eg $7.98 = {u_1}r$

attempt to express ${u_1}$ in terms of $r$ (or vice-versa) (M1)

eg ${u_1} = \frac{{7.98}}{r}$ , ${u_1} = 33.25\left( {1 - r} \right)$ , $r = \frac{{7.98}}{{{u_1}}}$ , $r = \frac{{33.25 - {u_1}}}{{33.25}}$

correct working (A1)

eg $\frac{{\left( {\frac{{7.98}}{r}} \right)}}{{1 - r}} = 33.25$ , $33.25\left( {1 - r} \right) = \frac{{7.98}}{r}$ , (0.4, 19.95), (0.6, 13.3), $\frac{{{u_1}}}{{1 - \frac{{7.98}}{{{u_1}}}}} = 33.25$

$r = 0.4\,\,\,\,\left( { = \frac{2}{5}} \right)$ , $r = 0.6\,\,\,\,\left( { = \frac{3}{5}} \right)$ A1A1 N3

[6 marks]

Examiners’ report

[N/A]