The nth rule is a formula that gives the value of any term in a sequence based on its position. The position of a term is represented by 'n', and the nth rule is often written as 'xn ± y'. In this formula:
- x represents the constant difference between consecutive terms in the sequence.
- y is a specific number that is added or subtracted from the product of 'x' and 'n'.
To find the nth rule for a sequence:
- Identify the pattern: Look for the difference between consecutive terms. This will be your 'x' value.
- Determine the value of y: Observe how the first term in the sequence relates to the product of 'x' and 1. This difference is 'y'.
- Write the rule: Combine the values of 'x' and 'y' in the formula 'xn ± y'.
Example:
Consider the sequence: 2, 5, 8, 11, 14...
- Pattern: Each term is 3 greater than the previous term (x = 3).
- Value of y: The first term is 2, and 3 * 1 = 3. To get 2 from 3, we need to subtract 1 (y = -1).
- Nth rule: The nth rule for this sequence is 3n - 1.
Therefore, the nth rule for the sequence 2, 5, 8, 11, 14... is 3n - 1.
Note: This explanation primarily focuses on arithmetic sequences where the difference between consecutive terms is constant.
