Sequences 2 (Edexcel GCSE Maths): Revision Notes

Sequences 2

What is an arithmetic sequence?

An arithmetic sequence (also called a linear sequence) is a sequence of numbers where the difference between consecutive terms stays the same. This constant difference is what makes the sequence arithmetic.

Finding the nth term formula

The nth term formula allows you to find any term in an arithmetic sequence without listing all the previous terms.

The general formula

$\text{nth term} = \text{Difference} \times n + \text{Zero term}$

Where:

• Difference = the constant difference between consecutive terms
• n = the position number of the term you want
• Zero term = the term that would come before the 1st term

Step-by-step method

Follow these steps to find the nth term formula for any arithmetic sequence:

Step 1: Write down the difference between consecutive terms

• Look at the sequence and find what you add each time

Step 2: Find the zero term

• Work backwards from the first term by subtracting the difference
• The zero term is what you would get if $n = 0$

Step 3: Write the formula

• Use: nth term = Difference × n + Zero term

Step 4: Simplify if needed

• Combine like terms to get the final formula

Using the nth term formula

Once you have the formula, you can perform several important operations:

Check if a number is in the sequence

• Substitute the number into your formula and solve for n
• If n is a positive whole number, the number is in the sequence
• If n is not a positive whole number, the number is not in the sequence

Generate any term in the sequence

• Substitute the position number (n) into your formula
• Calculate to find the value of that term

Exam tips

Remember!