The nth term is a rule that describes a sequence of numbers. It allows us to find any term in the sequence without having to list out all the terms before it.
Understanding Linear Sequences
Linear sequences have a constant difference between each term. This difference is called the common difference.
Finding the nth Term
nth term = (common difference * n) + (first term - common difference)
Example:
Let's find the nth term of the sequence 2, 5, 8, 11, 14...
nth term = (3 * n) + (2 - 3)
nth term = 3n - 1
Using the nth Term
Once you have the nth term formula, you can find any term in the sequence by substituting the desired value of 'n'.
10th term = (3 * 10) - 1
10th term = 30 - 1
10th term = 29
Practice Problems
Key Points
nth term = (common difference * n) + (first term - common difference)
.Remember: Practice makes perfect! Work through plenty of examples to gain confidence in finding the nth term.
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