Page 1 of 27 pages
MATHEMATICS:
Sequences and Series
Name: _______________ Surname: __________________
Class: ______
Issued: ________________________
Compiled by Kaleb
, Page 2 of 27 pages
Question 2
Given the arithmetic series: −7 − 3 + 1+ . . . +173
2.1 How many terms are there in the series? (3)
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2.2 Calculate the sum of the series. (3)
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2.3 Write this series in sigma notation. (3)
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[9]
Compiled by Kaleb
, Page 3 of 27 pages
Question 3
3.1 Consider the geometric sequence: 4 ; −2 ; 1 ; …
3.1.1 Determine the next term of the sequence. (2)
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1
3.1.2 Determine 𝑛 if the 𝑛𝑡ℎ term is . (4)
64
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3.1.3 Calculate the sum to infinity of the series: 4 − 2 + 1 … (2)
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3.2 If 𝑥 is a REAL number, show that the following sequence can NOT be
geometric: 1; 𝑥 + 1; 𝑥 − 3; … (4)
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[12]
Compiled by Kaleb
MATHEMATICS:
Sequences and Series
Name: _______________ Surname: __________________
Class: ______
Issued: ________________________
Compiled by Kaleb
, Page 2 of 27 pages
Question 2
Given the arithmetic series: −7 − 3 + 1+ . . . +173
2.1 How many terms are there in the series? (3)
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
2.2 Calculate the sum of the series. (3)
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
2.3 Write this series in sigma notation. (3)
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
[9]
Compiled by Kaleb
, Page 3 of 27 pages
Question 3
3.1 Consider the geometric sequence: 4 ; −2 ; 1 ; …
3.1.1 Determine the next term of the sequence. (2)
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________________________________________________________________
________________________________________________________________
1
3.1.2 Determine 𝑛 if the 𝑛𝑡ℎ term is . (4)
64
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
3.1.3 Calculate the sum to infinity of the series: 4 − 2 + 1 … (2)
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
3.2 If 𝑥 is a REAL number, show that the following sequence can NOT be
geometric: 1; 𝑥 + 1; 𝑥 − 3; … (4)
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________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
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[12]
Compiled by Kaleb
