6. Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
Tn : the nth term
7. Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
Tn : the nth term
S n : the sum of the first n terms
8. Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
Tn : the nth term
S n : the sum of the first n terms
e.g . Tn n 2 2, find;
9. Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
Tn : the nth term
S n : the sum of the first n terms
e.g . Tn n 2 2, find;
i T5
10. Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
Tn : the nth term
S n : the sum of the first n terms
e.g . Tn n 2 2, find;
i T5 52 2
27
11. Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
Tn : the nth term
S n : the sum of the first n terms
e.g . Tn n 2 2, find;
i T5 52 2 (ii) whether 42 is a term in the sequence
27
12. Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
Tn : the nth term
S n : the sum of the first n terms
e.g . Tn n 2 2, find;
i T5 52 2 (ii) whether 42 is a term in the sequence
27 42 n 2 2
13. Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
Tn : the nth term
S n : the sum of the first n terms
e.g . Tn n 2 2, find;
i T5 52 2 (ii) whether 42 is a term in the sequence
27 42 n 2 2
n 2 40
n 40
14. Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
Tn : the nth term
S n : the sum of the first n terms
e.g . Tn n 2 2, find;
i T5 52 2 (ii) whether 42 is a term in the sequence
27 42 n 2 2
n 2 40
n 40 , which is not an integer
Thus 42 is not a term
16. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
17. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
18. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a
19. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a
T3 T2
20. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a
T3 T2
d Tn Tn1
21. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2
d Tn Tn1
22. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2 T2 a d
d Tn Tn1
23. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2 T2 a d
d Tn Tn1 T3 a 2d
24. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2 T2 a d
d Tn Tn1 T3 a 2d
Tn a n 1d
25. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2 T2 a d
d Tn Tn1 T3 a 2d
Tn a n 1d
e.g .i If T3 9 and T7 21, find;
the general term.
26. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2 T2 a d
d Tn Tn1 T3 a 2d
Tn a n 1d
e.g .i If T3 9 and T7 21, find;
the general term.
a 2d 9
27. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2 T2 a d
d Tn Tn1 T3 a 2d
Tn a n 1d
e.g .i If T3 9 and T7 21, find;
the general term.
a 2d 9
a 6d 21
28. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2 T2 a d
d Tn Tn1 T3 a 2d
Tn a n 1d
e.g .i If T3 9 and T7 21, find;
the general term.
a 2d 9
a 6d 21
4d 12
d 3
29. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2 T2 a d
d Tn Tn1 T3 a 2d
Tn a n 1d
e.g .i If T3 9 and T7 21, find;
the general term.
a 2d 9
a 6d 21
4d 12
d 3 a 3
30. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2 T2 a d
d Tn Tn1 T3 a 2d
Tn a n 1d
e.g .i If T3 9 and T7 21, find;
the general term.
a 2d 9 Tn 3 n 13
a 6d 21
4d 12
d 3 a 3
31. Arithmetic Series
An arithmetic series is a sequence of numbers in which each term after
the first is found by adding a constant amount to the previous term.
The constant amount is called the common difference, symbolised, d.
d T2 a T1 a
T3 T2 T2 a d
d Tn Tn1 T3 a 2d
Tn a n 1d
e.g .i If T3 9 and T7 21, find;
the general term.
a 2d 9 Tn 3 n 13
a 6d 21 3 3n 3
4d 12 3n
d 3 a 3