linear sequences aim to find the nth term of a sequence
TRANSCRIPT
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Linear Sequences
AimAimTo find the nth term of a sequence
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Mapping Diagrams
2nn21426384
What do you notice?
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Mapping Diagrams
2nn21426384
Same difference each timeDifference is 2
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Mapping Diagrams
4n - 1n3172113154
What do you notice?
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Mapping Diagrams
4n - 1n3172113154
Same differencedifference is 4
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Generating a sequence for 2n + 5
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm2n + 5
•An expression can be used to produce a sequence.
•It is referred to as the nth term
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Generating a sequence for 2n + 5
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm2n + 5
(2 x 1 + 5) = 7
7
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Generating a sequence for 2n + 5
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm2n + 5
(2 x 2 + 5) = 9
97
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Generating a sequence for 2n + 5
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm2n + 5
(2 x 3 + 5) = 11
117 9
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Generating a sequence for 2n + 5
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm2n + 5
(2 x 4 + 5) = 13
11117 9 13
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Generating a sequence for 2n + 5
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm2n + 5117 9 1
513
The sequence generated by 2n + 5 is
7, 9, 11, 13, 15, …….What do you notice?
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Generating a sequence for 2n + 5
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm2n + 5
(2 x 5 + 5) = 15
11117 9 15
13
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Generate a sequence for 4n + 3
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm4n + 3
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Generate a sequence for 4n + 3
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm
7 11 15 19 23 4n + 3
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Activity: Complete the sequences
TERM 1st 2nd 3rd 4th 5th …nth
6n – 4 5n + 22n + 7n – 4n + 2
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Solutions
n + 276543
n – 410-1-2-3
2n + 7171513119
5n + 2272217127
6n – 4 26201482
nth…5th4th3rd2nd1stTERM
127
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What if…..
• We knew the sequence, how could we find the nth term?
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Finding the nth term
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm
8 10 12 14 16
How much is each term increasing by?
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Finding the nth term
TERM1st term
2nd
term
3rd
term
4th
term
5th
term …nthterm
8 10 12 14 16
+ 2
+ 2
+ 2
+ 2
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Finding the nth term
TERM
1st term
2nd
term
3rd
term
4th
term
5th
term …nthterm
8 10 12 14 16
The common difference is 2.
The nth term begins with 2n
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Finding the nth term
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm
8 10 12 14 16
2 4 6 8 10 2n
The sequence generated by 2n is
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Finding the nth term
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm
8 10 12 14 16
2 4 6 8 10 2n
What would I need to add to the second sequence so that it is equal to the first sequence?
+ ?
+ ?
+ ?
+ ?
+ ?
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Finding the nth term
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm
8 10 12 14 16
2 4 6 8 10 2n
I would need to add 6 to each term
+ 6
+ 6
+ 6
+ 6
+ 6
+ 6
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Finding the nth term
TERM1st term
2nd
term3rd
term4th
term5th
term …nthterm
8 10 12 14 162n + 6
2 4 6 8 10 2n
I would need to add 6 to each term
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If…..
• The nth term is 5n – 1, how could I find the value of the 100th term?Either I could write out all the terms until I reached the 100th term.
OR
I could substitute n for 100.100th term is (5 x 100) – 1 = 499