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Date May 2019 Marks available 5 Reference code 19M.2.SL.TZ2.S_10
Level Standard Level Paper Paper 2 Time zone Time zone 2
Command term Find Question number S_10 Adapted from N/A

Question

In an arithmetic sequence, u1=1.3u2=1.4 and uk=31.2.

Consider the terms, un, of this sequence such that nk.

Let F be the sum of the terms for which n is not a multiple of 3.

Find the exact value of Sk.

[2]
b.

Show that F=3240.

[5]
c.

An infinite geometric series is given as S=a+a2+a2+aZ+.

Find the largest value of a such that S<F.

[5]
d.

Markscheme

correct substitution      (A1)

eg   3002(1.3+31.2)3002[2(1.3)+(3001)(0.1)]3002[2.6+299(0.1)] 

Sk=4875        A1  N2

[2 marks]

b.

recognizing need to find the sequence of multiples of 3 (seen anywhere)       (M1)

eg   first term is u3 (= 1.5)   (accept notation u1=1.5) ,

d=0.1×3  (= 0.3) , 100 terms (accept n=100), last term is 31.2

(accept notation u100=31.2) ,  u3+u6+u9+  (accept F=u3+u6+u9+)

correct working for sum of sequence where n is a multiple of 3      A2

1002(1.5+31.2) ,  50(2×1.5+99×0.3) ,  1635

valid approach (seen anywhere)       (M1)

eg    Sk(u3+u6+) ,  Sk1002(1.5+31.2)Sk (their sum for (u3+u6+))

correct working (seen anywhere)       A1

eg   Sk1635 , 4875 − 1635

F=3240       AG  N0

[5 marks]

c.

attempt to find r       (M1)

eg    dividing consecutive terms

correct value of r (seen anywhere, including in formula)

eg   12 ,  0.707106… ,  a0.293

correct working (accept equation)        (A1)

eg   a112<3240

correct working     A1

 

METHOD 1 (analytical)

eg   3240×(112) ,  a<948.974 ,  948.974

METHOD 2 (using table, must find both S values)

eg   when a=948 ,  S=3236.67  AND  when a=949 ,  S=3240.08

a=948       A1  N2

[5 marks]

d.

Examiners report

[N/A]
b.
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c.
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d.

Syllabus sections

Topic 1—Number and algebra » SL 1.2—Arithmetic sequences and series
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