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Subjects · Leaving Cert Maths

Leaving Cert Maths: Sequences & series

How often Sequences & series comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker

OL Asked on 9 of the last 10 Ordinary Level papers, most recently in 2026. banker

FL Asked on 3 of the last 7 Foundation Level papers, most recently in 2026.

Sequences & series, Higher Level(6 marks)

Quick ones on Sequences & series.

(a)General term Tₙ of an arithmetic sequence?
  1. a + nd
  2. a + (n − 1)d
  3. arⁿ⁻¹
(b)Sum to infinity of a geometric series (−1 < r < 1)?
  1. a(1 − r)
  2. a/(r − 1)
  3. a/(1 − r)
(c)Next term: 3, 6, 12, 24, …
  1. 48
  2. 30
  3. 36
Show the answers

(a) a + (n − 1)d

(b) a/(1 − r)

(c) 48

Your turn: Higher Level questions on Sequences & series.

Higher Level

Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Paper 1, Q2, Paper 1, Q6, Paper 1, Q9
2025Paper 1, Q7, Paper 1, Q10
2024Paper 1, Q5
2023Paper 1, Q8, Paper 1, Q10
2022Paper 1, Q4, Paper 1, Q9
2021Paper 1, Q4, Paper 1, Q7, Paper 1, Q10
2019Paper 1, Q7
2018Paper 1, Q2, Paper 1, Q5, Paper 1, Q9, Paper 2, Q7
2017Paper 1, Q4, Paper 1, Q8
2016Paper 1, Q9

Links open the State Examinations Commission’s paper for that year.

More Sequences & series questions

Sequences & series, 2 marks

Sum to infinity of 9 + 3 + 1 + …?

  1. 13
  2. 27
  3. 13.5
Show the answer

13.5

Geometric with a = 9 and r = 1/3, so S∞ = 9/(1 − 1/3) = 9/(2/3) = 13.5.

Sequences & series, 2 marks

1 + 2 + 3 + … + 100 = ?

  1. 10100
  2. 5050
  3. 5000
Show the answer

5050

Arithmetic series: Sₙ = (n/2)(first + last) = (100/2)(1 + 100) = 50 × 101 = 5050.

Sequences & series, 2 marks

A geometric series has a sum to infinity when …

  1. −1 < r < 1
  2. r > 1
  3. r < 0
Show the answer

−1 < r < 1

Only then do the terms shrink towards 0, so the sum settles at a finite value, a/(1 − r).

Ordinary Level

Asked on 9 of the last 10 Ordinary Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Q5
2025Q9
2024Q8
2023Not asked
2022Q6
2021Q6, Q9
2019Q8
2018Q4, Q7
2017Q7
2016Q5

Links open the State Examinations Commission’s paper for that year.

More Sequences & series questions

Sequences & series, 2 marks

Next term: 5, 9, 13, 17, …

  1. 20
  2. 22
  3. 21
Show the answer

21

The terms go up by 4 each time, so the next is 17 + 4 = 21.

Sequences & series, 2 marks

An arithmetic sequence has a = 3 and d = 5. Find T₄.

  1. 20
  2. 18
  3. 23
Show the answer

18

Tₙ = a + (n − 1)d, so T₄ = 3 + 3 × 5 = 18. Use n − 1, not n.

Sequences & series, 2 marks

Next term: 2, 6, 18, 54, …

  1. 162
  2. 108
  3. 72
Show the answer

162

Each term is 3 times the one before, so 54 × 3 = 162.

Foundation Level

Asked on 3 of the last 7 Foundation Level papers, most recently in 2026.

Every paper, year by year

YearWhere it came up
2026Q4
2025Q7
2024Not asked
2023Not asked
2022Not asked
2021Not asked
2019Q3

Links open the State Examinations Commission’s paper for that year.

More Sequences & series questions

Sequences & series, 2 marks

What is the next number in the pattern 5, 9, 13, 17, …?

  1. 22
  2. 20
  3. 21
Show the answer

21

The pattern goes up by 4 each time. 17 + 4 = 21.

Sequences & series, 2 marks

The number of squares in a pattern goes 4, 7, 10, 13, … What type of sequence is this?

  1. Doubling
  2. Linear
  3. Non-linear
Show the answer

Linear

It goes up by the same amount (3) every time, so it is linear.

Sequences & series, 2 marks

Number of squares = 4n − 3. How many squares are in pattern 10?

  1. 37
  2. 43
  3. 7
Show the answer

37

Put n = 10: 4 × 10 − 3 = 40 − 3 = 37.

Other Maths topics

All of Leaving Cert Maths