2.3 Sequences
Sequences
Everything on sequences that can come up in the WJEC GCSE Mathematics and Numeracy, in Unit 2 and Unit 3. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
A worked example
Continuing a sequence · [2 marks]
Here are the first four terms of a sequence: 5, 14, 23, 32. Write down the next two terms.
- B141
- B150
The exam skills (10)
Continuing a sequence
- Find the difference between terms.
- Keep adding (or subtracting) it.
- Check the rule works for every term.
Watch out: Getting the sign wrong in a decreasing sequence.
Using the nth term
- Replace n with the term number.
- Work it out with BIDMAS.
- That is the term.
Watch out: Writing 2n with n = 8 as 28. It means 2 × 8.
Nth term
- The difference goes in front of n.
- Work out what to add or take away to get the first term.
- Check with the second term.
Watch out: Using the first term as the number in front of n.
Is it in the sequence?
- Set the nth term equal to the number.
- Solve for n.
- A whole number means yes; a decimal or fraction means no.
Watch out: Answering yes or no with no working. The method mark is the equation.
Which term?
- Find the nth term.
- Set it equal to the number you are looking for.
- Solve: n is the position.
Watch out: Giving the value when the question asks for the position.
Geometric sequence
- Divide a term by the one before to find the multiplier.
- Keep multiplying.
- The multiplier can be a fraction or negative.
Watch out: Looking for a difference. Geometric sequences multiply.
Fibonacci-type sequence
- Each term = the two before it added together.
- Keep going until you reach the term you need.
- Count the terms carefully.
Watch out: Adding the term to itself.
First negative term
- Find the nth term.
- Solve nth term < 0.
- Take the next whole number for n, then work out that term.
Watch out: Giving the last positive term instead of the first negative one.
Quadratic nth term
- Find the second difference and halve it: that is the number in front of n².
- Take that n² part away from each term.
- Find the nth term of what is left and add it on.
Watch out: Using the second difference itself in front of n². Halve it.
Quadratic sequence
- Set the nth term equal to the value.
- Rearrange to = 0 and solve the quadratic.
- Only a positive whole number n is a position.
Watch out: Giving both solutions. A term number cannot be negative.
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