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Date May 2017 Marks available 4 Reference code 17M.1.AHL.TZ2.H_3
Level Additional Higher Level Paper Paper 1 Time zone Time zone 2
Command term Find Question number H_3 Adapted from N/A

Question

The 1st, 4th and 8th terms of an arithmetic sequence, with common difference d , d 0 , are the first three terms of a geometric sequence, with common ratio r . Given that the 1st term of both sequences is 9 find

the value of d ;

[4]
a.

the value of r ;

[1]
b.

Markscheme

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

EITHER

the first three terms of the geometric sequence are 9 , 9 r and 9 r 2      (M1)

9 + 3 d = 9 r ( 3 + d = 3 r ) and 9 + 7 d = 9 r 2      (A1)

attempt to solve simultaneously     (M1)

9 + 7 d = 9 ( 3 + d 3 ) 2

OR

the 1 st , 4 th and 8 th terms of the arithmetic sequence are

9 ,   9 + 3 d ,   9 + 7 d      (M1)

9 + 7 d 9 + 3 d = 9 + 3 d 9      (A1)

attempt to solve     (M1)

THEN

d = 1      A1

[4 marks]

a.

r = 4 3      A1

 

Note:     Accept answers where a candidate obtains d by finding r first. The first two marks in either method for part (a) are awarded for the same ideas and the third mark is awarded for attempting to solve an equation in r .

 

[1 mark]

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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