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Sequences
The Term-to-Term Rule
Here is a list of numbers
3, 6,12, 24, 48
What is the rule for going from one term to the
next?
That’s right – double it!
Now try to find rules for these sequences of
numbers:
1, 4, 7, 10, 13
66, 56, 46, 36, 26
200, 100, 50, 25,12.5
1, 3, 7, 15, 31
5, 1, -3, -7, -11
2, -4, 8, -16, 32
The answers are:
1, 4, 7, 10, 13
Add 3
66, 56, 46, 36, 26
Subtract 10
200, 100, 50, 25, 12.5
Divide by 2 (halve it)
1, 3, 7, 15, 31
Double, then add 1
5, 1, -3, -7, -11
Subtract 4
2, -4, 8, -16, 32
Multiply by -2 (tricky one, that!)
SEQUENCES
THE POSITION-TO-TERM FORMULA
Look at this formula:
t = 2n + 3
What do the letters stand for?
t stands for the value of a particular term
n stands for the position of that term
See how the formula leads to the sequence
For the first number in the sequence, n = 1
So the first term is (2 x 1) + 3, which is 5
For the second number in the sequence, n = 2
So the second term is (2 x 2) + 3, which is 7
Check the other three terms shown
Question: What would the tenth term in the
sequence be?
The answer is 23, because (2 x 10) +3 = 23
Question: What would the hundredth term in the
sequence be?
The answer is 203, because (2 x 100) + 3 = 203
Now see if you can find the first 5
terms for each of these sequences:
t = 3n – 1
t = 5n
t=n+6
t = 4n + 2
t = 10n – 9
t = ½n
The answers are:
t = 3n – 1
2, 5, 8, 11, 14...
t = 5n
5, 10, 15, 20, 25...
t=n+6
7, 8, 9, 10, 11...
t = 4n + 2
6, 10, 14, 18, 22...
t = 10n – 9
1, 11, 21, 31, 41...
t = ½n
½, 1, 1 ½, 2, 2 ½...