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Date November 2010 Marks available 6 Reference code 10N.1.hl.TZ0.5
Level HL only Paper 1 Time zone TZ0
Command term Find Question number 5 Adapted from N/A

Question

The mean of the first ten terms of an arithmetic sequence is 6. The mean of the first twenty terms of the arithmetic sequence is 16. Find the value of the 15th term of the sequence.

Markscheme

METHOD 1

5(2a+9d)=60 (or 2a+9d=12)     M1A1

10(2a+19d)=320 (or 2a+19d=32)     A1

solve simultaneously to obtain     M1

a=3, d=2     A1

the 15th term is 3+14×2=25     A1

Note: FT the final A1 on the values found in the penultimate line.

 

METHOD 2

with an AP the mean of an even number of consecutive terms equals the mean of the middle terms     (M1)

a10+a112=16(or a10+a11=32)     A1

a5+a62=6(or a5+a6=12)     A1

a10a5+a11a6=20     M1

5d+5d=20

d=2 and a=3(or a5=5 or a10=15)     A1

the 15th term is 3+14×2=25(or 5+10×2=25 or 15+5×2=25)     A1

Note: FT the final A1 on the values found in the penultimate line.

 

[6 marks]

Examiners report

Many candidates had difficulties with this question with the given information often translated into incorrect equations.

Syllabus sections

Topic 1 - Core: Algebra » 1.1 » Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.
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