1. Linear sequences
A linear sequence is a name for a list of numbers where the next number is found by adding or subtracting a constant number. Here is an example:
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2. 5, 8, +3
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3. 5, 8, 11, +3 +3
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4. 5, 8, 11, 14 +3 +3 +3
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5. 5, 8, 11, 14, 17…
etc +3 +3 +3 +3
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6. 1 2 3 4 5 8 11 14 17 Finding the a rule for the nth term Position (n)
This is a rule that connects a term’s position (n) with its value.
Position (n) 1 2 3 4 5
Value 8 11 14 17
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7. Find the nth rule for this sequence: 5, 8, 11, 14, 17…
Make a table with 5 columns and write the position of the terms – 1st 2nd 3rd 4th etc as the n numbers in the first column n 1 2 3 4 5
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8. Put the terms into the second column, 5, 8, 11, 14, 17…2 8 3 11 4 14 17 6
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9. Find the difference between the terms 8 – 5 = 3 and write it in the third column1 5 3 2 8 11 4 14 17 6
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10. Write the difference number multiplied by the n number in the fourth column
Term
Difference 3n 1 5 3 2 8 6 11 9 4 14 12 17 15
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11. Write the difference between the value of 3n and the term in the fifth column
Term – 3n 1 5 3 2 8 6 11 9 4 14 12 17 15
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12. The nth rule is:
Term = 3n + 2
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13. n
Term = 3n + 2
Term 1
3 X 1 + 2 5 2
3 X 2 + 2 8 3
3 X 3 + 2 11 4
3 X 4 + 2 14
3 X 5 + 2 17
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D. Smith