EDEXCEL GCSE FOUNDATION MATHS - What is the Nth Term

EDEXCEL GCSE Foundation Maths - What is the Nth Term?

The nth term is a formula that allows you to find any term in a sequence without having to write out the entire sequence. Let's break it down!

Understanding Sequences

A sequence is a list of numbers that follow a specific pattern. For example:

• 2, 4, 6, 8, 10... (This is the sequence of even numbers)
• 3, 6, 9, 12, 15... (This is the sequence of multiples of 3)

The Formula

The nth term formula is usually written in the form: an + b

• n represents the position of the term in the sequence (e.g., 1st term, 2nd term, 3rd term, etc.)
• a represents the common difference between terms in the sequence (the amount you add or subtract to get to the next term).
• b represents the value of the first term in the sequence when n = 1.

Finding the nth Term

Let's find the nth term of the sequence 2, 4, 6, 8, 10...

1. Find the common difference (a): Each term is 2 more than the previous term, so a = 2.

2. Find the value of the first term when n = 1 (b): The first term is 2, so b = 2.

3. Write the nth term formula: Substituting the values of a and b, the nth term formula is 2n + 2.

Using the nth Term Formula

Now that we have the nth term formula, we can find any term in the sequence.

• To find the 5th term: Substitute n = 5 into the formula: 2(5) + 2 = 12. The 5th term is 12.

• To find the 10th term: Substitute n = 10 into the formula: 2(10) + 2 = 22. The 10th term is 22.

Practice Time

Find the nth term of the following sequences:

1. 5, 8, 11, 14...
2. 7, 10, 13, 16...

Key Points

• The nth term formula is a powerful tool for finding any term in a sequence.
• Practice finding the nth term for different sequences to get comfortable with the formula.
• Remember that the nth term formula can also be used to generate sequences.