| Date | May 2018 | Marks available | 3 | Reference code | 18M.2.sl.TZ2.4 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
The first term of an infinite geometric sequence is 4. The sum of the infinite sequence is 200.
Find the common ratio.
Find the sum of the first 8 terms.
Find the least value of n for which Sn > 163.
Markscheme
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]
