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1. The nth
term of a sequence: How to do It
How to find the general rule of a sequence:
The sequence is 05, 09, 13, 17. The difference between all of the numbers is 4
and if you take away 4 from the first number the sequence, the answer is 1. So
the nth
term or general rule is 4n + 1.
How to find the th/st/nd
number in a sequence: multiply that number by the
amount of ‘n’ in the general rule and add or minus the second number in the
general rule. An example: the sequence is 04, 06,08,10,12. The general rule is
2n+2. To find the 15th
term in the sequence multiply 15 by 2n which is 30. 30 +
2 is 32. A and 32 is the 15th
term in the sequence.
Find the first 5 terms in the sequence:
Say if you have 3n – 1. Multiply 1 by three and take- away 1 ( 3x1=3. Then 3-1
=2. So the first number in the sequence is 2.)
For the second term: 3x2=6. 6-1=5. The second number in the sequence is 5.
For the third term: (3x3) – 1 = 8
Fourth term: (3x4) – 1 = 11
Fifth term: (3x5) – 1 = 14
So the sequence is: 2,5,8,11,14

2. The nth
term: Question I
Find the nth
term of the sequence:
a) 07,12,17,22,27 nth term= __________________
b) -1,02,05,08,11 nth term=___________________
c) 08,15,22,29 nth term=___________________
d) -1,5,11,17,23 nth term=___________________
e) 03,05,07,09,11 nth term=___________________
f) -1,4,9,14,19 nth term=___________________
The nth
term: Question II
Find the 20th
,25th
and 50th
term of the sequence:
a) 06,09,12,15,18,21 50th
:
25th
:
20th
:
b) 13,17,21,25,29 50th
:
25th
:
20th
:
c) 07,04,01,-2,-5 50th
:
25th
:
20th
:
d) 08,05,02,-1,-4 50th
:
25th
:
20th
:
The nth
term: Question III
Write the first 5 terms in the sequence (with all workings)
a) n + 2
Answer:_____________________________

3. b) 5n + 2
Answer:_____________________________
c) 5n + 2
Answer:_____________________________
d) 4n – 7
Answer:_____________________________
e) 10n + 9
Answer:_____________________________