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Understanding Number Sequences: Linear Sequences and Nth Term Rule

Learn about sequences and rules connecting numbers. Explore linear sequences and discover how to find the Nth term rule for a given sequence.

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Understanding Number Sequences: Linear Sequences and Nth Term Rule

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  1. Sequences Monday, 06 January 2020 A sequence is a list of numbers. There is usually some rule that connects these numbers. The numbers are sometimes called terms. For example: 3, 7, 11, 15… You add on 4 to get the next number (term) 1, 2, 4, 8, 16… You double to get the next number (term)

  2. Try to write down the next three terms for each of these sequences and describe the rule.

  3. 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:

  4. 5, 8, +3

  5. 5, 8, 11, +3 +3

  6. 5, 8, 11, 14 +3 +3 +3

  7. 5, 8, 11, 14, 17… etc +3 +3 +3 +3

  8. Finding the a rule for the nth term This is a rule that connects a term’s position (n) with its value.

  9. 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

  10. Put the terms into the second column, 5, 8, 11, 14, 17…

  11. Find the difference between the terms 8 – 5 = 3 and write it in the third column +3

  12. Write the difference number multiplied by the n number in the fourth column +3

  13. Write the difference between the value of 3n and the term in the fifth column +3 The nth term rule =3n+ 2

  14. Put the terms into the second column,

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