A-Level · Mathematics · AQA · Mark scheme decoded
AQA A-Level Mathematics: Arithmetic Sequences and Series — mark scheme explained
The short answer
Understanding and working with arithmetic sequences and series is a fundamental part of A-Level Mathematics. An arithmetic sequence (or arithmetic progression) is a sequence in which each term after the first is obtained by adding a constant, called the common difference ( d ), to the preceding term.
The question
Find the 12th term of the arithmetic sequence where the first term is 8 and the common difference is 3. [Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Identify the given values: a 1 = 8 , d = 3 , n = 12
- S2
Use the formula for the n-th term of an arithmetic sequence: a n = a 1 + (n - 1)d
- S3
Substitute the values into the formula: a 12 = 8 + (12 - 1) × 3
- S4
Simplify the expression: a 12 = 8 + 11 × 3 = 8 + 33 = 41
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Identify the given values: a 1 = 8 , d = 3 , n = 12
- S2
Use the formula for the n-th term of an arithmetic sequence: a n = a 1 + (n - 1)d
- S3
Substitute the values into the formula: a 12 = 8 + (12 - 1) × 3
- S4
Simplify the expression: a 12 = 8 + 11 × 3 = 8 + 33 = 41
Final answer: The 12th term is 41.
Common mistakes
- Using the wrong formula for the n-th term or sum of an arithmetic series. — Always double-check the problem statement to determine whether you need the n-th term or the sum of the series, and use the appropriate formula.
- Forgetting to subtract 1 from n in the n-th term formula. — Always remember to use (n - 1) in the formula for the n-th term.
- Incorrectly substituting values into the formulas. — Double-check your substitutions and calculations to ensure accuracy. Use a calculator if necessary.
- Using the common difference instead of the first term in the sum formula. — Ensure you are using the correct values for a 1 and d in the sum formula.
- Forgetting to divide by 2 in the sum formula. — Always remember to divide by 2 when using the sum formula S n = n/2 [2a 1 + (n - 1)d] or S n = n/2 (a 1 + a n ) .
- Using the wrong value for n in the formulas. — Always verify that you are using the correct value for n based on the problem statement.
- Forgetting to simplify expressions before calculating the final answer. — Take your time to simplify expressions step-by-step before calculating the final answer.
Where the marks go
- Full worked solution (all marking points)3 marks