Date | May 2017 | Marks available | 6 | Reference code | 17M.2.SL.TZ2.S_5 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 2 |
Command term | Find | Question number | S_5 | Adapted from | N/A |
Question
Consider a geometric sequence where the first term is 768 and the second term is 576.
Find the least value of n such that the nth term of the sequence is less than 7.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
attempt to find r (M1)
eg576768, 768576, 0.75
correct expression for un (A1)
eg768(0.75)n−1
EITHER (solving inequality)
valid approach (accept equation) (M1)
egun<7
valid approach to find n M1
eg768(0.75)n−1=7, n−1>log0.75(7768), sketch
correct value
egn=17.3301 (A1)
n=18 (must be an integer) A1 N2
OR (table of values)
valid approach (M1)
egun>7, one correct crossover value
both crossover values, u17=7.69735 and u18=5.77301 A2
n=18 (must be an integer) A1 N2
OR (sketch of functions)
valid approach M1
egsketch of appropriate functions
valid approach (M1)
egfinding intersections or roots (depending on function sketched)
correct value
egn=17.3301 (A1)
n=18 (must be an integer) A1 N2
[6 marks]