18M.2.SL.TZ2.S_4

pestleMathematicsAISLPaper 218M· sl-1-3-geometric-sequences-and-seriessource ↗

The first term of an infinite geometric sequence is 4. The sum of the infinite sequence is 200.

Find the common ratio.

[2]

Find the sum of the first 8 terms.

[2]

Find the least value of n for which S_n > 163.

[3]

Markscheme / solution

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

correct substitution into infinite sum (A1)
eg $200 = \frac{4}{{1 - r}}$

r = 0.98 (exact) A1 N2

[2 marks]

correct substitution (A1)

$\frac{{4\left( {1 - {{0.98}^8}} \right)}}{{1 - 0.98}}$

29.8473

29.8 A1 N2

[2 marks]

attempt to set up inequality (accept equation) (M1)
eg $\frac{{4\left( {1 - {{0.98}^n}} \right)}}{{1 - 0.98}} > 163,\,\,\frac{{4\left( {1 - {{0.98}^n}} \right)}}{{1 - 0.98}} = 163$

correct inequality for n (accept equation) or crossover values (A1)
eg n > 83.5234, n = 83.5234, S₈₃ = 162.606 and S₈₄ = 163.354

n = 84 A1 N1

[3 marks]

Examiners’ report

[N/A]