Is the nth term of a sequence on the Foundation paper too?

Yes. The nth term of a linear sequence is crossover content, so it is set on both tiers, and Foundation students also meet Fibonacci type sequences and simple geometric progressions. Higher tier adds the nth term of a quadratic sequence and geometric progressions whose common ratio is a surd.

How many marks is an nth term question worth on Edexcel Higher?

The expression on its own is usually 2 marks: one for the correct coefficient of n, one for the correct constant. A follow-up part asking whether a number is a term is typically another 2 marks, and an algebraic Fibonacci type question can run to 5 or 6 marks across three parts.

Do I get the nth term formula on the Edexcel formulae sheet?

No. Sequences are not on the formulae sheet, so you deduce the rule from the common difference every time. For an arithmetic sequence with first term a and common difference d the nth term is a + (n - 1)d, though most students are quicker writing dn and adjusting the constant.

What is the difference between a term-to-term rule and a position-to-term rule?

A term-to-term rule tells you how to get from one term to the next, such as 'add 6' or 'multiply by 3', so you need the previous term before you can use it. A position-to-term rule, which is what the nth term is, goes straight from the position to the term: put n = 40 in and the 40th term drops out. Edexcel names both in A23 and can ask for either.

nth Term of a Sequence - Edexcel GCSE Higher Maths

Typically 2-5 marks per paper, often inside the first three questions · Spec 1MA1

An nth term rule turns a position into a term: put $n = 50$ into $7n - 2$ and you have the 50th term without writing out the 49 before it. Edexcel's 1MA1 specification spreads this over three references. A23 is generating terms from a term-to-term or a position-to-term rule, A24 names the families you have to recognise (arithmetic progressions, Fibonacci type sequences and geometric progressions), and A25 is deducing the nth term itself. The linear nth term is crossover content that Foundation students also meet; geometric progressions with a surd ratio, and the nth term of a quadratic sequence (which has its own page), are Higher only.

On a Higher paper a linear sequence usually turns up early, worth 2 marks for the expression, and it is frequently followed by a part asking whether a given number is a term of the sequence. Fibonacci type sequences tend to arrive in algebraic dress: three terms written $a$ , $b$ , $a + b$ , then two conditions to solve together. Geometric progressions can appear on any of the three papers, but Paper 1 is non-calculator, so a ratio there will be something you can multiply by hand, while Papers 2 and 3 are free to use a ball bouncing to 60% of its height or a population tripling every hour.

The two marks for a linear rule split cleanly: one for an expression of the form $7n + k$ , one for the right value of $k$ . That is why $7n + 2$ still banks a mark and $n + 7$ banks nothing. The second mark in a membership question goes for the sentence, not the sum: solving $7n - 2 = 200$ to get $n = 28.857\ldots$ is only half the answer, and the mark is for saying that $n$ is not a whole number, so 200 is not a term. Practise decreasing sequences separately, because $8 - 6n$ regularly comes back as $6 - 8n$ or $6n + 8$ .

Worked example

Here are the first four terms of an arithmetic sequence.

5, \quad 12, \quad 19, \quad 26

(a) Write an expression, in terms of

n

, for the nth term of this sequence. (2 marks) (b) Is 200 a term of this sequence? Show how you get your answer. (2 marks)

[4 marks]

The terms go up by 7 each time, so the rule starts with $7n$ .
M1: common difference used as the coefficient of $n$ , giving an expression of the form $7n + k$
$7n$ generates 7, 14, 21, 28. The sequence is 2 less each time, so the nth term is $7n - 2$ .
A1: fully correct expression; the check is $n = 4$ giving $28 - 2 = 26$
If 200 were a term then $7n - 2 = 200$ , so $7n = 202$ .
M1: forming and starting to solve an equation, which beats listing terms towards 200
$n = \frac{202}{7} = 28.857\ldots$ , which is not a whole number, so 200 is not a term of the sequence.
A1: correct $n$ with the conclusion written down; the mark is for the reason, not the division

Practice questions

These are original questions in Edexcel 1MA1 Higher style. The linear, Fibonacci type and small geometric questions are all designed to work without a calculator, which is how Paper 1 sets them; the growth and decay contexts near the harder end assume Paper 2 or Paper 3. Type expressions like 7n - 2 straight into the box, and any equivalent form is accepted.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [2 marks]

Here are the first four terms of an arithmetic sequence. $5, \quad 9, \quad 13, \quad 17$ Write an expression, in terms of $n$ , for the nth term of this sequence.

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 2 Warm-up [2 marks]

The nth term of a sequence is $8n - 3$ . Work out the 25th term.

Your answer (fractions like 1/2 are fine)
Question 3 Exam pace [2 marks]

Here are the first four terms of an arithmetic sequence. $20, \quad 17, \quad 14, \quad 11$ Write an expression, in terms of $n$ , for the nth term of this sequence.

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 4 Exam pace [2 marks]

The first three terms of a geometric progression are $4, \quad 12, \quad 36$ Work out the 6th term.

Your answer (fractions like 1/2 are fine)
Question 5 Exam pace [3 marks]

A pattern of squares is made from matchsticks. Pattern 1 uses 4 matchsticks, pattern 2 uses 7 matchsticks and pattern 3 uses 10 matchsticks. The pattern continues in the same way. How many matchsticks are used in pattern 25?

Your answer (fractions like 1/2 are fine)
Question 6 Stretch [4 marks]

The first four terms of a Fibonacci sequence are $a, \quad 2a, \quad 3a, \quad 5a$ The sum of the first five terms of this sequence is 228. Work out the value of $a$ .

Your answer (fractions like 1/2 are fine)

Common mistakes examiners see

Writing $n + 7$ for 5, 12, 19, 26, using the common difference as the number you add rather than the coefficient of $n$ . It scores zero, because it is not of the form $7n + k$ .

Find the difference and write it in front of the $n$ before doing anything else. The difference is the coefficient; the constant is whatever you then need so that $n = 1$ gives the first term.
Getting the constant the wrong way round, $7n + 2$ instead of $7n - 2$ . That keeps the method mark and loses the accuracy mark.

Substitute $n = 1$ into the finished rule and compare with the first term. $7(1) - 2 = 5$ matches the sequence; $7(1) + 2 = 9$ does not.
Solving $7n - 2 = 200$ , getting $n = 28.857\ldots$ , rounding it to 29 and answering yes.

A position has to be a whole number, so the decimal is the answer, not a problem to tidy up. Write 'n is not an integer, so 200 is not a term of the sequence' as your final line.
Reversing a decreasing sequence. For 2, -4, -10, -16 the rule is $8 - 6n$ , but $6 - 8n$ and $6n + 8$ both appear often, and some students generate the sequence by subtracting 8 rather than 6.

Carry the sign into the coefficient, write $-6n$ first, then work out the constant that repairs the first term. Testing $n = 1$ in $6 - 8n$ gives $-2$ , not 2, which catches it in seconds.
Hunting for a common difference in 3, 6, 12, 24 and offering $3n$ , when consecutive terms are being multiplied by 2 rather than added to.

Check differences and ratios before you pick a method. A constant difference means arithmetic and a rule $dn + k$ ; a constant ratio means geometric, and terms come from repeated multiplication.

Frequently asked questions

Is the nth term of a sequence on the Foundation paper too?: Yes. The nth term of a linear sequence is crossover content, so it is set on both tiers, and Foundation students also meet Fibonacci type sequences and simple geometric progressions. Higher tier adds the nth term of a quadratic sequence and geometric progressions whose common ratio is a surd.
How many marks is an nth term question worth on Edexcel Higher?: The expression on its own is usually 2 marks: one for the correct coefficient of $n$ , one for the correct constant. A follow-up part asking whether a number is a term is typically another 2 marks, and an algebraic Fibonacci type question can run to 5 or 6 marks across three parts.
Do I get the nth term formula on the Edexcel formulae sheet?: No. Sequences are not on the formulae sheet, so you deduce the rule from the common difference every time. For an arithmetic sequence with first term $a$ and common difference $d$ the nth term is $a + (n - 1)d$ , though most students are quicker writing $dn$ and adjusting the constant.
What is the difference between a term-to-term rule and a position-to-term rule?: A term-to-term rule tells you how to get from one term to the next, such as 'add 6' or 'multiply by 3', so you need the previous term before you can use it. A position-to-term rule, which is what the nth term is, goes straight from the position to the term: put $n = 40$ in and the 40th term drops out. Edexcel names both in A23 and can ask for either.

nth Term of a Sequence - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics