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Class notes

Arithmetic Sequences and Series

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The notes aims to provide a comprehensive overview of arithmetic sequences and series, including theory, problem-solving strategies, and real-world applications, tailored to the Grade 12 CAPS curriculum requirements. It contains a blank copy as well as STEP BY STEP SOLUTIONS

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Document information

  • February 16, 2024
  • 42
  • 2023/2024
  • Class notes
  • Mr. p hermanus
  • All classes

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Page 1


ARITHMETIC SEQUENCES AND SERIES




3 ; 8 ; 13 ; … (ARITHMETIC SEQUENCE)


3 ; 9 ; 27 ; … (GEOMETRIC SEQUENCE)


SEQUENCE: A SET OF REAL NUMBERS IN A _______________________ IS
CALLED A SEQUENCE.




𝑇1 ; 𝑇2 ; 𝑇3 ; 𝑇4 ; … ; 𝑇𝑛
; ; ; ; … ;
; ; ; ; … ;
; ; ; ; … ;
; ; ; ; … ;


ARITHMETIC SEQUENCE:
If and are real numbers, then
; ; ; ;
is an arithmetic sequence with:
𝑎=
𝑑=
𝑇𝑛 =

, Page 2


1. Find the 4th term of the arithmetic sequence:
7 ; 3 ; …
Solution:




1 1
2. Find 𝑇10 of 4 ; 1 ; −1 ; −3
2 2
Solution:

, Page 3


3. Find the 7th term of the sequence 2 ; 5 ; 8 ; …
Solution:




Do a check:
𝑇1 𝑇2 𝑇3 𝑇4 𝑇5 𝑇6 𝑇7

, Page 4


3 1
4. Find the 8th term of the sequence −4 ; −1 ; ; …
4 2
Solution:




REVERSE PROCESS !
5. Which term of the sequence 4 ; 9 ; 14 ; … will be 34?
Solution:

, Page 5


6. How many terms are there in the sequence 3 ; 7 ; 11 ; … ; 147
Solution:




7. Which term of the arithmetic sequence 10 ; 7 ; … is −5?
Solution:

, Page 6


8. How many terms are there in the sequence:

3 1 3
45 ; 43 ; 42 ; … ; 33
4 2 4
Solution:

, Page 7


SIMULTANEOUS EQUATIONS
9. The 12th term of an arith. sequence is −5 and the 20th term is 7.
Find the 7th term.
Solution:

, Page 8


10. The 7th term of an arith. sequence is 20 and the 13 th term is 38.
Find the first 3 terms.
Solution:

, Page 9


11. In an arith. sequence the 7 th term is 30 and the 4th term is 18.
Find the 1st term and the common difference.
Solution:

, Page 10


12. Find the 20th term of an arith. sequence if the 5 th term is 11 and the
12th term is 25.
Solution:

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