linear sequences slideshow 7, room 307 mr richard sasaki, mathematics slideshow 7, room 307 mr...
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Answers Yen (or 12) 1050ml 5 (naan bread and tandoori chicken)TRANSCRIPT
Linear Sequences
Slideshow 7, Room 307Mr Richard Sasaki, Mathematics
• Find patterns in sequences• Make formulae for sequences (the n-
th term)• Use formulae to find positions of
certain numbers
Objectives
First, please try the 5 minute vocabulary check. The purpose of this is to not fall for decoy information, good luck!
Answers5
5
240 Yen
5
7
4
3
15 (or 12)
1050ml
5 (naan bread and tandoori chicken)
SequencesA sequence is an ordered number pattern. It is often easy to see which numbers are missing in the pattern or the next numbers that come.
3, 5, 7, 9, __, 13, __, __11 15 17Here it was easy to tell that the numbers increase by 2 every step to the right.If numbers go up (or down) in the same way every step, then the sequence is linear.
SequencesWith sequences, it is important to understand each number’s position.
3, 5, 7, 9, __, 13, __, __11 15 171 2 3 4 5 6 7 8
We call the position .So for the second position (where ), we have 5.How about the 20th position ()?Well done! But what calculation did we do to get to 41?
2041
PositionNumber
SequencesThe formula must be “in terms of” . This means that the formula must be about .
3, 5, 7, 9, __, 13, __, __11 15 171 2 3 4 5 6 7 8 20
41PositionNumber
Let’s try to make a formula for this sequence. 𝑛
The formula must contain the unknown as we relate it to each number’s position.The formula goes up in twos. So we need to multiply the unknown by 2.
2 Is that it?Let’s check.
( means .)
SequencesIf the formula is , we multiply (the position) by .𝑛2 3, 5, 7, 9, __, 13, __, __11 15 17
1 2 3 4 5 6 7 8PositionNumber2𝑛 2,4, 6,8,10,12,14, 16
All of the numbers in our test are slightly off, how much by?
+1
We need to add 1 to each.Example
Find a formula in terms of for the sequence below.7, 10, 13, 16, 19, …
Finished!
The numbers increase by each time.3𝑛3…?
Sequences
7, 10, 13, 16, 19, …1 2 3 4 5Position
Number𝑛3…?
A quicker way to do this is to find the 0th term. 0
__,4We simply add the 0th term to our formula.
+4
Using , we can reproduce our sequence to check if it is correct.
3𝑛+4𝑛=17, 𝑛=210,𝑛=313,It looks good!
Sequences
3
ExampleFind a formula for the nth term for the sequence below. Also, find out what the 50th term is.
2, 7, 12, 17, 22, …How much do the numbers increase by?
5What would the 0th term be?
-3,
-3What is the formula for the nth term? -𝑛5
What would the 50th term be?5𝑛 –3 ,𝑛=50
(5×50)−3247
¿247
Answers - Easy8 1214
1 4 1950 6266
21 3339-5-3 32 -10 -14
258
0.5-327
10
-51
-4
− 1372𝑛+2
Answers - Medium32
3𝑛+2
2𝑛+15𝑛8𝑛−50.5𝑛+1
−3𝑛−42𝑛7 −
137
102228406𝑛−2
6×10−2=586×100−2=5985 ,7 ,9 ,11 ,132×50+3=103
Answers - Hard6
12 166 9
4.55.5-1-2
-56746 𝑎
1, 5, 9, 13, 17, 21, 25, 294×35−3=137
, …5811
2𝑛𝑛+13𝑛+1
𝑛+32𝑛+83𝑛−3𝑛+2.5−𝑛+211𝑛−16−3𝑛+132𝑎𝑛
3𝑛+2