Arithmetic Sequences
What is an arithmetic progression?
- In an arithmetic progression (also called arithmetic sequence), the difference between consecutive terms in the sequence is constant
- This constant difference is known as the common difference, d, of the sequence
- For example, 1, 4, 7, 10, … is an arithmetic sequence with the rule ‘start at one and add three to each number’
- The first term, a, is 1
- The common difference, d, is 3
- An arithmetic progression can be increasing (positive common difference) or decreasing (negative common difference)
- Each term of an arithmetic progression is referred to by the letter u with a subscript determining its place in the sequence
How do I find a term in an arithmetic progression?
- The nth term formula for an arithmetic progression is given as
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- Where is the first term, and is the common difference
- This is given on the list of formulas page of the exam, you do not need to know how to derive it
- Sometimes you will be given a term and asked to find the first term or the common difference
- Substitute the information into the formula and solve the equation
- Sometimes you will be given two terms and asked to find both the first term and the common difference
- Substitute the information into the formula and set up two simultaneous equations
- Solve the simultaneous equations
Examiner Tip
- Simultaneous equations are often needed within arithmetic progression questions
- Make sure you are confident solving them