Sub-topic 1
2025 · National One-Eighth
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Sum to infinity of $1+0.1+0.01+0.001+\ldots$ and $20-2+0.2-0.02+\ldots$
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Sub-topic 2
2025 · National One-Eighth
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First term and common difference given $u_3=23$ and $u_6=11$
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Sub-topic 3
2024 · National Preliminary
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Exponential sequence $x+5$, $x+3$, $\dfrac{x+7}{3}$: values of $x$, common ratio and sum to infinity
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Sub-topic 4
2017 · National One-Eighth
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First term and common difference given $u_9=26$ and $u_{20}=59$
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Sub-topic 5
2025 · National One-Eighth
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Inserting three numbers between $-17$ and $7$ to form a linear sequence
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Sub-topic 6
2024 · National One-Eighth
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General term $u_n=s_n-s_{n-1}$ from $s_n=n^2$, $s_n=n(n+1)$ and $s_n=n^2-2n$ (true/false)
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Sub-topic 7
2024 · National Preliminary
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First term and common difference given $u_3=6$ and $u_6=15$
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Sub-topic 8
2026 · National One-Eighth
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Terms $u_3$, $u_4$ and $u_5$ from the recurrence $u_{n+2}=u_{n+1}\pm u_n$
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Sub-topic 9
2025 · National Semifinal
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First term and common difference given $s_4=36$ and $u_7=24$
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Sub-topic 10
2026 · National Quarterfinal
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Common difference of a linear sequence with terms $x-4$, $2x-4$ and $6-2x$
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Sub-topic 11
2026 · National Preliminary
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Common difference of a linear sequence with terms $x+2$, $2x-2$ and $10-x$
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Sub-topic 12
2026 · National One-Eighth
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Common ratio of a geometric sequence with terms $x+1$, $x$ and $x-2$
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Sub-topic 13
2026 · National One-Eighth
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Common difference of a linear sequence with terms $2x-3$, $x+7$ and $15-x$
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Sub-topic 14
2025 · National Quarterfinal
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Fixed point of the recurrence $u_{n+1}=3u_n-6$
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Sub-topic 15
2023 · National One-Eighth
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Convergence of a geometric series to infinity when $|r|\lt1$ (true/false)
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Sub-topic 16
2021 · National Preliminary
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Sum to infinity of $2+\dfrac{6}{4}+\dfrac{18}{16}+\ldots$ and similar geometric series
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Sub-topic 17
2024 · National Preliminary
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Sum to infinity of a geometric series (second set)
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Sub-topic 18
2021 · National Preliminary
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First term and common difference given $u_2=5$ and $u_7=-5$
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Sub-topic 19
2024 · National One-Eighth
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Riddle: pascal's triangle
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Sub-topic 20
2026 · National Preliminary
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Is $2+3+5+8+13+\ldots$ a linear (arithmetic) series? (true/false)
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Sub-topic 21
2003 · National Semifinal
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Three numbers in arithmetic progression with sum $15$ and product $45$
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Sub-topic 22
2003 · National Semifinal
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Three numbers in arithmetic progression with sum $27$ and third minus first equal to $16$
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Sub-topic 23
2013 · National Preliminary
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Finding $x$ when $x-4$, $x+2$ and $3x+1$ are consecutive terms of an arithmetic progression
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Sub-topic 24
2013 · National Preliminary
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Finding $x$ when $x-1$, $x+1$ and $x+9$ are consecutive terms of a geometric progression
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Sub-topic 25
2013 · National Preliminary
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Finding $x$ when $x$, $x+1$ and $x+4$ are consecutive terms of a geometric progression
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Sub-topic 26
2014 · National Quarterfinal
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Next two terms of $30,\ 29,\ 27,\ 24,\ 20,\ \ldots$
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Sub-topic 27
2014 · National Quarterfinal
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Next two terms of $5,\ 7,\ 10,\ 14,\ 19,\ \ldots$
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Sub-topic 28
2014 · National Quarterfinal
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Next two terms of $3,\ 8,\ 13,\ 18,\ \ldots$
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Sub-topic 29
2016 · National Preliminary
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Next term of $1,\ 2,\ 4,\ 7,\ 11,\ \ldots$
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Sub-topic 30
2018 · National Preliminary
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Three consecutive even integers whose sum is $30$ more than twice the middle number
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Sub-topic 31
2019 · National Preliminary
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General term of $-5,\ -2,\ 1,\ 4,\ 7,\ \ldots$
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Sub-topic 32
2021 · National Preliminary
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Fourth term of a sequence with $s_n=n^2+3n+2$
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Sub-topic 33
2021 · National Semifinal
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General term of an exponential sequence with $u_5=80$ and $u_8=640$
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Sub-topic 34
2022 · National Preliminary
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Constant sequence with $u_n=2u_{n-1}+3$
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Sub-topic 35
2022 · National Preliminary
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Finding $n$ such that the sum of $24+20+16+12+8+\ldots$ is zero
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Sub-topic 36
2022 · National Preliminary
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Riddle: a sequence — a function on the natural numbers, arithmetic/geometric/linear/exponential
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Sub-topic 37
2023 · National Preliminary
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First three terms of the sequence $u_n=3n^2-2n$
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Sub-topic 38
2023 · National One-Eighth
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Exponential sequence $3,a,b,c,48$: finding $a$, $b$ and $c$
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