Paper 1 June 2025, Question 6 2 marks
An arithmetic series has first term 3 and common difference – 0.5
Find the sum of the first 250 terms.
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AQA A Level Maths
Topic questions Pure mathematics Arithmetic sequences and series
Arithmetic sequences and series
7 questions · 47 marks · about 1 hour
Arithmetic sequences and series questions
TopicArithmetic sequences and series▾
AQA 7357 Arithmetic sequences and series 7 questions
Paper 1 June 2024, Question 10 6 marks
(a)
[2]
An arithmetic sequence has 300 terms.
The first term of the sequence is –7 and the last term is 32
Find the sum of the 300 terms.
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(b)
[4]
A school holds a raffle at its summer fair.
There are nine prizes.
The total value of the prizes is £1260
The values of the prizes form an arithmetic sequence.
The top prize has the highest value, and the bottom prize has the least value.
The value of the top prize is six times the value of the bottom prize.
Find the value of the top prize.
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Paper 2 June 2023, Question 5 7 marks
Ziad is training to become a long-distance swimmer.
He trains every day by swimming lengths at his local pool.
The length of the pool is 25 metres.
Each day he increases the number of lengths that he swims by four.
On his first day of training, Ziad swims 10 lengths of the pool.
(a)
[1]
Write down an expression for the number of lengths Ziad will swim on his n th day of training.
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(b)(i)
[3]
Ziad’s target is to be able to swim at least 3000 metres in one day.
Determine the minimum number of days he will need to train to reach his target.
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(b)(ii)
[3]
Ziad’s coach claims that when he reaches his target he will have covered a total distance of over 50 000 metres.
Determine if Ziad’s coach is correct.
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Paper 1 June 2022, Question 9 9 marks
The first three terms of an arithmetic sequence are given by
(a)
[3]
Show that x 
5 is the only value which gives an arithmetic sequence.
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(b)(i)
[1]
Write down the value of the first term of the sequence.
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(b)(ii)
[1]
Find the value of the common difference of the sequence.
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(c)
[4]
The sum of the first N terms of the arithmetic sequence is SN where
Find the value of N.
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Paper 1 November 2021, Question 6 7 marks
(a)
[4]
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(b)
[3]
The sum of the first n terms of this series is Tn
Find the value of n such that Tn 
Sn
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Paper 1 June 2019, Question 5 7 marks
An arithmetic sequence has first term a and common difference d.
The sum of the first 16 terms of the sequence is 260
(a)
[2]
Show that 4a 
30d 65
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(b)
[3]
Given that the sum of the first 60 terms is 315, find the sum of the first 41 terms.
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(c)
[2]
Sn is the sum of the first n terms of the sequence.
Explain why the value you found in part (b) is the maximum value of Sn
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Paper 1 June 2018, Question 9 9 marks
An arithmetic sequence has first term a and common difference d.
The sum of the first 36 terms of the sequence is equal to the square of the sum of the first 6 terms.
(a)
[4]
Show that 4a 70d 4a2 
20ad 
25d2
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(b)
[5]
Given that the sixth term of the sequence is 25, find the smallest possible value of a.
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