The document defines a geometric series as a sequence of numbers where each subsequent term is found by multiplying the previous term by a constant ratio. The constant ratio is called the common ratio and is represented by r. Examples are provided to demonstrate calculating terms of a geometric series given the first term and common ratio. The concept of finding the first term greater than a given value is also illustrated.

1. Geometric Series

2. Geometric SeriesAn geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.

3. Geometric SeriesAn geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.

4. Geometric Series
a
T
r 2

An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.

5. Geometric Series
a
T
r 2

2
3
T
T

An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.

6. Geometric Series
a
T
r 2

2
3
T
T

An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r

7. Geometric Series
a
T
r 2

2
3
T
T

aT 1
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r

8. Geometric Series
a
T
r 2

2
3
T
T

aT 1
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r
arT 2

9. Geometric Series
a
T
r 2

2
3
T
T

aT 1
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r
arT 2
2
3 arT 

10. Geometric Series
a
T
r 2

2
3
T
T

aT 1
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r
arT 2
2
3 arT 
1
 n
n arT

11. Geometric Series
a
T
r 2

2
3
T
T

aT 1
  32,8,2,oftermgeneraltheandFind.. rige
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r
arT 2
2
3 arT 
1
 n
n arT

12. Geometric Series
a
T
r 2

2
3
T
T

aT 1
  32,8,2,oftermgeneraltheandFind.. rige
4,2  ra
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r
arT 2
2
3 arT 
1
 n
n arT

13. Geometric Series
a
T
r 2

2
3
T
T

aT 1
  32,8,2,oftermgeneraltheandFind.. rige
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r
arT 2
2
3 arT 
1
 n
n arT
1
 n
n arT 4,2  ra

14. Geometric Series
a
T
r 2

2
3
T
T

aT 1
  32,8,2,oftermgeneraltheandFind.. rige
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r
arT 2
2
3 arT 
1
 n
n arT
1
 n
n arT
  1
42


n
4,2  ra

15. Geometric Series
a
T
r 2

2
3
T
T

aT 1
  32,8,2,oftermgeneraltheandFind.. rige
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r
arT 2
2
3 arT 
1
 n
n arT
1
 n
n arT
  1
42


n
 
  22
12
22
22




n
n
4,2  ra

16. Geometric Series
a
T
r 2

2
3
T
T

aT 1
  32,8,2,oftermgeneraltheandFind.. rige
4,2  ra
An geometric series is a sequence of numbers in which each term after
the first is found by multiplying a constant amount to the previous
term.
The constant amount is called the common ratio, symbolised, r.
1

n
n
T
T
r
arT 2
2
3 arT 
1
 n
n arT
1
 n
n arT
  1
42


n
 
  22
12
22
22




n
n 12
2 
 n
nT

17.   rTTii find,49and7If 42 

18.   rTTii find,49and7If 42 
7ar

19.   rTTii find,49and7If 42 
7ar
493
ar

20.   rTTii find,49and7If 42 
7ar
493
ar
72
r

21.   rTTii find,49and7If 42 
7ar
493
ar
72
r
7r

22.   rTTii find,49and7If 42 
7ar
(iii) find the first term of 1, 4, 16, … to
be greater than 500.
493
ar
72
r
7r

23.   rTTii find,49and7If 42 
7ar
(iii) find the first term of 1, 4, 16, … to
be greater than 500.
493
ar
72
r
7r
4,1  ra

24.   rTTii find,49and7If 42 
7ar
(iii) find the first term of 1, 4, 16, … to
be greater than 500.
493
ar
72
r
7r
4,1  ra   1
41


n
nT

25.   rTTii find,49and7If 42 
7ar
(iii) find the first term of 1, 4, 16, … to
be greater than 500.
500nT
493
ar
72
r
7r
4,1  ra   1
41


n
nT

26.   rTTii find,49and7If 42 
7ar
(iii) find the first term of 1, 4, 16, … to
be greater than 500.
500nT
5004 1
n
493
ar
72
r
7r
4,1  ra   1
41


n
nT

27.   rTTii find,49and7If 42 
7ar
(iii) find the first term of 1, 4, 16, … to
be greater than 500.
500nT
5004 1
n
493
ar
72
r
7r
4,1  ra   1
41


n
nT
500log4log 1
n

28.   rTTii find,49and7If 42 
7ar
(iii) find the first term of 1, 4, 16, … to
be greater than 500.
500nT
5004 1
n
  500log4log1 n
493
ar
72
r
7r
4,1  ra   1
41


n
nT
500log4log 1
n

29.   rTTii find,49and7If 42 
7ar
(iii) find the first term of 1, 4, 16, … to
be greater than 500.
500nT
5004 1
n
  500log4log1 n
48.5
48.41


n
n
493
ar
72
r
7r
4,1  ra   1
41


n
nT
500log4log 1
n

30.   rTTii find,49and7If 42 
7ar
(iii) find the first term of 1, 4, 16, … to
be greater than 500.
500nT
5004 1
n
  500log4log1 n
48.5
48.41


n
n
500first termtheis,10246 T
493
ar
72
r
7r
4,1  ra   1
41


n
nT
500log4log 1
n

31.   rTTii find,49and7If 42 
7ar
(iii) find the first term of 1, 4, 16, … to
be greater than 500.
500nT
5004 1
n
  500log4log1 n
48.5
48.41


n
n
500first termtheis,10246 T
Exercise 6E; 1be, 2cf, 3ad, 5ac, 6c, 8bd, 9ac, 10ac, 15, 17,
18ab, 20a
493
ar
72
r
7r
4,1  ra   1
41


n
nT
500log4log 1
n