18N.2.AHL.TZ0.H_1

pestleMathematicsAIHLPaper 218N· sl-1-3-geometric-sequences-and-seriessource ↗

Consider a geometric sequence with a first term of 4 and a fourth term of −2.916.

Find the common ratio of this sequence.

[3]

Find the sum to infinity of this sequence.

[2]

Markscheme / solution

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

${u_4} = {u_1}{r^3} \Rightarrow - 2.916 = 4{r^3}$ (A1)

solving, $r = - 0.9$ (M1)A1

[3 marks]

${S_\infty } = \frac{4}{{1 - \left( { - 9} \right)}}$ (M1)

$= \frac{{40}}{{19}}\,\left( { = 2.11} \right)$ A1

[2 marks]

Examiners’ report

[N/A]