|
|
sequencesequence  An example of a sequence from Handel's Acis and Galatea. | In music, a device allowing key modulation favoured by early keyboard composers in which a phrase is repeated sequentially, each time transposing to a different key. |
sequence To find the rule for extending the pattern in a number sequence, state the action to reach each previous term for the next term. | List of numbers that are generated by a rule. Each number in the sequence is a term. For example, 3, 7, 11, 15, 19 is a sequence of five terms generated by adding 4 to the previous term. To generate a sequence, it is necessary to know the first term, the number of terms in the sequence, and the rule. |
| Examples of special sequences include: |
| even numbers 2, 4, 6, 8, 10... the rule is add 2 |
| square numbers 1, 4, 9, 16, 25... the rule is 12, 22, 32, and so on |
| triangle numbers 1, 3, 6, 10, 15... the rule is 1, 1 + 2, 1 + 2 + 3, and so on |
Finding the formula The rule for a sequence only relates one term to the next term in the sequence. In order to find any term (the nth term, where n ≥ 1) in the sequence, it is necessary to find a formula that relates the term to its position in the sequence. This can be done by finding the common difference between the terms. |
| For example, to find the formula for the 20th term in the sequence 3, 7, 11, 15, 19..., a table can be drawn up: |
| The formula in this case for the nth term is 4 × the position number − 1, which can be written as 4n − 1, where n stands for the position number. Using the formula, the 20th term will be 4 × 20 − 1 = 79. |
How to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit webmaster's page for free fun content. |
?Sign in  |
|---|
|
|
|
)
)