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Date May 2018 Marks available 3 Reference code 18M.1.AHL.TZ2.H_5
Level Additional Higher Level Paper Paper 1 Time zone Time zone 2
Command term Find Question number H_5 Adapted from N/A

Question

The geometric sequence u1, u2, u3, … has common ratio r.

Consider the sequence  A = { a n = lo g 2 | u n | : n Z + } .

Show that A is an arithmetic sequence, stating its common difference d in terms of r.

[4]
a.

A particular geometric sequence has u1 = 3 and a sum to infinity of 4.

Find the value of d.

[3]
b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

METHOD 1

state that  u n = u 1 r n 1 (or equivalent)      A1

attempt to consider a n and use of at least one log rule       M1

lo g 2 | u n | = lo g 2 | u 1 | + ( n 1 ) lo g 2 | r |       A1

(which is an AP) with d = lo g 2 | r | (and 1st term lo g 2 | u 1 | )      A1

so A is an arithmetic sequence      AG

Note: Condone absence of modulus signs.

Note: The final A mark may be awarded independently.

Note: Consideration of the first two or three terms only will score M0.

[4 marks]

 

METHOD 2

consideration of  ( d = ) a n + 1 a n       M1

( d ) = lo g 2 | u n + 1 | lo g 2 | u n |

( d ) = lo g 2 | u n + 1 u n |      M1

( d ) = lo g 2 | r |      A1

which is constant      R1

Note: Condone absence of modulus signs.

Note: The final A mark may be awarded independently.

Note: Consideration of the first two or three terms only will score M0.

a.

attempting to solve  3 1 r = 4      M1

r = 1 4      A1

d = 2      A1

[3 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

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

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