Date | November 2021 | Marks available | 2 | Reference code | 21N.2.SL.TZ0.6 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Find | Question number | 6 | Adapted from | N/A |
Question
The sum of the first n terms of a geometric sequence is given by Sn=nΣr=123(78)r.
Find the first term of the sequence, u1.
Find S∞.
Find the least value of n such that S∞-Sn<0.001.
Markscheme
u1=S1=23×78 (M1)
=1424(=712=0.583333…) A1
[2 marks]
r=78(=0.875) (A1)
substituting their values for u1 and r into S∞=u11-r (M1)
=143(=4.66666…) A1
[3 marks]
attempt to substitute their values into the inequality or formula for Sn (M1)
143-nΣr=123(78)r<0.001 OR Sn=712(1-(78)n)(1-78)
attempt to solve their inequality using a table, graph or logarithms
(must be exponential) (M1)
Note: Award (M0) if the candidate attempts to solve S∞-un<0.001.
correct critical value or at least one correct crossover value (A1)
63.2675… OR S∞-S63=0.001036… OR S∞-S64=0.000906…
OR S∞-S63-0.001=0.0000363683… OR S∞-S64-0.001=0.0000931777…
least value is n=64 A1
[4 marks]