IB Maths AI SL · Unit 1: Number and Algebra
Exam-style IB Maths AI SL sequences and series questions with worked solutions. Start with the 5 fully worked examples below — each is solved step by step the way an IB examiner expects — then try the practice questions and check your working against the mark scheme.
Common difference, nth term, and sum formulas. In SL AI these are almost always dressed up as a real-world context: seat rows in a stadium, monthly salary rises, or step-by-step savings. Arithmetic sequences and series overview →
Geometric progressions underpin every SL AI compound interest, depreciation, and finance question. Mastering the r < 1 vs r > 1 case unlocks half of Paper 2's financial modelling questions. Geometric sequences and compound interest overview →
The question bank covers these sequences and series question types (number of questions in brackets):
An arithmetic sequence has a first term of $u_1 = 12$ and a common difference of $d = 4$. Find $u_{25}$.
1. Recall $u_n = u_1 + (n - 1)d$.
2. Substitute $u_1 = 12$, $d = 4$, $n = 25$.
3. Set up: $u_{25} = 12 + (25 - 1)(4)$.
4. Simplify the bracket: $u_{25} = 12 + (24)(4)$.
5. Evaluate: $u_{25} = 12 + 96 = \mathbf{108}$.
A ball is dropped from $10\text{ m}$. After each bounce it rebounds to $80\%$ of its previous height. Calculate the total vertical distance travelled from the moment it is dropped until it hits the ground for the 6th time.
1. Recognise the initial drop is $10\text{ m}$ (down only). The 5 subsequent rebounds are up-and-down each.
2. Identify the rebound sequence: $u_1 = 10 \times 0.8 = 8\text{ m}$, $r = 0.8$.
3. Use $S_n = \frac{u_1(1 - r^n)}{1 - r}$ with $n = 5$.
4. Evaluate: $S_5 = \frac{8(1 - 0.8^5)}{0.2} = \frac{8(0.67232)}{0.2} = 26.8928\text{ m}$.
5. Total: initial drop $+\ 2 \times$ (sum of rebounds) $= 10 + 2(26.8928)$.
6. State: total distance $= 63.7856 \implies \mathbf{63.8\text{ m}}$.
An infinite geometric series has $u_1 = 18$ and common ratio $r = 0.6$. Find the exact sum to infinity.
1. Recall $S_\infty = \frac{u_1}{1 - r}$.
2. Check convergence: $|0.6| < 1$, so $S_\infty$ exists.
3. Substitute: $S_\infty = \frac{18}{1 - 0.6}$.
4. Simplify: $S_\infty = \frac{18}{0.4}$.
5. Evaluate: $\mathbf{S_\infty = 45}$.
An arithmetic sequence has $u_1 = 5$ and $d = 2$. Find the minimum number of terms required for the sum of the series to strictly exceed $150$.
1. Recall: $S_n = \frac{n}{2}(2u_1 + (n - 1)d)$.
2. Set up: $\frac{n}{2}(2(5) + (n - 1)2) > 150$.
3. Simplify: $\frac{n}{2}(2n + 8) > 150$.
4. Expand: $n^2 + 4n > 150 \implies n^2 + 4n - 150 > 0$.
5. Solve $n^2 + 4n - 150 = 0$ on the GDC: positive root $n \approx 10.42$.
6. Conclude: smallest integer $n = \mathbf{11}$.
Sequence A is arithmetic with $u_n = 50 + 10n$. Sequence B is geometric with $v_n = 20(1.5)^n$. Find the smallest integer $n$ for which $v_n$ is strictly greater than $u_n$.
1. Set up the inequality: $20(1.5)^n > 50 + 10n$.
2. Recognise that mixing exponential and linear forces a graphical/numerical solve.
3. Enter $Y_1 = 20(1.5)^x$ and $Y_2 = 50 + 10x$ on the GDC.
4. Use the intersection tool (G-Solv $\to$ ISCT).
5. Read: intersection at $x = 4.098\ldots$
6. Conclude: smallest integer $n = \mathbf{5}$.
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
An arithmetic sequence has the following first three terms: \(4, 9, 14, \dots\)
Find the common difference, \(d\).
Find the value of the 15th term, \(u_{15}\).
Find the sum of the first 15 terms of the sequence, \(S_{15}\).
Using the summation tool on your Graphic Display Calculator, evaluate the following arithmetic series: \[\sum_{k=1}^{12} (5k - 2)\] Show the values you entered into your calculator.
How many terms of the arithmetic series \(11 + 16 + 21 + 26 + \dots\) are needed to strictly exceed a sum of \(450\)? Use your GDC to solve.
There are 37 exam-style sequences and series questions in the AI SL question bank (Paper 1: 24 · Paper 2: 13), graded 6 easy, 12 medium, 7 hard, 8 very hard, 4 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Both. In the bank, Paper 1: 24 · Paper 2: 13. Practise with your GDC — AI papers expect calculator methods throughout.
Open the AI SL Unit 1 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.