Here's a breakdown:
* Sequence: A sequence is a list of numbers that follow a specific pattern. Examples:
* 2, 4, 6, 8, 10... (even numbers)
* 1, 3, 5, 7, 9... (odd numbers)
* 1, 4, 9, 16, 25... (square numbers)
* nth term: This formula usually involves a variable 'n', which represents the position of the term in the sequence. For example, 'n = 1' would be the first term, 'n = 2' would be the second term, and so on.
* Direct Calculation: The nth term formula allows you to calculate any term by substituting the desired value of 'n' into the formula.
Examples:
* Arithmetic Sequence: The nth term of an arithmetic sequence is given by:
* a_n = a_1 + (n-1)d
where:
* a_n is the nth term
* a_1 is the first term
* d is the common difference
* Geometric Sequence: The nth term of a geometric sequence is given by:
* a_n = a_1 * r^(n-1)
where:
* a_n is the nth term
* a_1 is the first term
* r is the common ratio
Benefits of the nth term:
* Predicting terms: You can find any term in the sequence without having to calculate the terms before it.
* Understanding the pattern: The formula reveals the underlying pattern of the sequence.
* Generalizing the sequence: The nth term represents a general formula that works for any term in the sequence.
Let me know if you have any other questions!