EDEXCEL GCSE FOUNDATION MATHS - What is the Nth Term

Edexcel GCSE Foundation Maths: What is the nth Term?

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.

• Example: 2, 5, 8, 11, 14...
  • The common difference is 3 (5-2 = 3, 8-5 = 3, etc.)

Finding the nth Term

1. Identify the common difference: Subtract any term from the one that follows it.
2. Write the general formula: The nth term of a linear sequence is:
3. nth term = (common difference * n) + (first term - common difference)
4. Substitute the values: Replace the common difference and the first term with their respective values.

Example:

Let's find the nth term of the sequence 2, 5, 8, 11, 14...

1. Common difference: 3
2. General formula: nth term = (3 * n) + (2 - 3)
3. Substitution: 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'.

• Example: To find the 10th term of the sequence 2, 5, 8, 11, 14..., we substitute n = 10 into the formula:
• 10th term = (3 * 10) - 1
• 10th term = 30 - 1
• 10th term = 29

Practice Problems

1. Find the nth term of the sequence 4, 7, 10, 13...
2. Find the 15th term of the sequence 1, 6, 11, 16...
3. What is the 20th term of the sequence 3, 8, 13, 18...?

Key Points

• The nth term is a rule that describes a sequence of numbers.
• It can be used to find any term in the sequence.
• Linear sequences have a constant difference between each term (the common difference).
• The general formula for the nth term of a linear sequence is: 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.