Date | May 2019 | Marks available | 2 | Reference code | 19M.2.SL.TZ1.S_7 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 1 |
Command term | Find | Question number | S_7 | Adapted from | N/A |
Question
The first terms of an infinite geometric sequence, un, are 2, 6, 18, 54, …
The first terms of a second infinite geometric sequence, vn, are 2, −6, 18, −54, …
The terms of a third sequence, wn, are defined as wn=un+vn.
The finite series, 225∑k=1wk , can also be written in the form m∑k=04rk.
Write down the first three non-zero terms of wn.
Find the value of r.
Find the value of m.
Markscheme
attempt to add corresponding terms (M1)
eg 2+2,6+(−6),2(3)n−1+2(−3)n−1
correct value for w5 (A1)
eg 324
4, 36, 324 (accept 4 + 36 + 324) A1 N3
[3 marks]
valid approach (M1)
eg 4×r1=36, 4×9n−1
r=9 (accept m∑k=04×9k; m may be incorrect) A1 N2
[2 marks]
recognition that 225 terms of wn consists of 113 non-zero terms (M1)
eg 113∑1, 112∑0, 113
m=112 (accept 1∑k=0124×rk; r may be incorrect) A1 N2
[2 marks]