Unit 1: Number and Algebra
Topic 1.2: Arithmetic Sequences and Series Questions
Practice 20 exam-style questions for IB Math AA SL Topic 1.2. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Find2 marks
2023
The sum of the first n terms of an arithmetic sequence is given by Sn = 2n2 + 3n.
Find the sum of the first 5 terms.
Find the sum of the first 5 terms.
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2023
The th term of a sequence is , where .
Write down an expression for .
Write down an expression for .
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2022
The nth term of an arithmetic sequence is given by un = 2.5n + 1.
State the value of the first term, u1.
State the value of the first term, u1.
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2023
A student receives a grant of 1240 euros on the first day of each month for five years.
Find the total amount paid.
Find the total amount paid.
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2025
An arithmetic sequence has first term 45 and common difference -5.
The sum of the first n terms of this sequence is zero. Find the value of n.
The sum of the first n terms of this sequence is zero. Find the value of n.
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2024
The 2nd, 5th and 8th terms of an arithmetic sequence are , and respectively.
Show that .
Show that .
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2021
A fund holds 4200 euros at the start of the first month and falls by 175 euros every month, so the amounts form an arithmetic sequence.
Given that the balance in the kth month is zero, find the value of k.
Given that the balance in the kth month is zero, find the value of k.
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2021
An arithmetic sequence has first term 72 and common difference −4.5.
Given that the kth term of the sequence is zero, find the value of k.
Given that the kth term of the sequence is zero, find the value of k.
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2023
The sum of the first n terms of an arithmetic sequence is given by Sn = 5n − n2.
Given that S4 = 4, find the value of u4.
Given that S4 = 4, find the value of u4.
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2025
A wall is built in rows of bricks. The top row has 5 bricks and every row below has 4 more bricks than the row above it. Let tn be the number of bricks in row n.
Find t4.
Find t4.
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2023
A tenant pays rent of 2750 euros on the first day of each month for four years.
Find the total amount paid.
Find the total amount paid.
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2025
An arithmetic sequence has first term 21 and common difference -3.
The sum of the first n terms of this sequence is zero. Find the value of n.
The sum of the first n terms of this sequence is zero. Find the value of n.
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2022
The th term of an arithmetic sequence is given by .
State the value of the first term, .
State the value of the first term, .
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2026
A theatre has 24 seats in the front row, and each row behind has 4 more seats than the row in front.
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2022
The nth term of an arithmetic sequence is given by un = 42 − 5n.
Find the common difference, d.
Find the common difference, d.
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2025
A pattern of dots grows in stages. Stage 1 has 3 dots, stage 2 has 8 dots and stage 3 has 15 dots; each stage adds a row that is two dots longer than the row added before it. Let tn be the number of dots in stage n.
Find t4.
Find t4.
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2022
The nth term of an arithmetic sequence is given by un = 4n − 9.
State the value of the first term, u1.
State the value of the first term, u1.
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2022
The nth term of an arithmetic sequence is given by un = 4n − 9.
Find the common difference, d.
Find the common difference, d.
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2022
The first three terms of an arithmetic sequence are ln y, (3/4) ln y and (1/2) ln y, where y > 1.
Write down the common difference in the form k ln y, where k is a rational number.
Write down the common difference in the form k ln y, where k is a rational number.
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2024
In an arithmetic sequence, u3 = 7 and u8 = 32.
Find d.
Find d.
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