SL 1.2—Arithmetic sequences and series Questionbank

Practice SL 1.2—Arithmetic sequences and series with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SL & HLPaper 1

In an arithmetic progression the sum of the first six terms is $75$ and the sum of the next six terms is $183$ .

Find the common difference and the first term.

[5]

Question 2

SL & HLPaper 1

The $n$ th term of an arithmetic progression is given by $u_n = 24 - 2n$ .

State the value of the initial term, $a$ .

[1]

Given that the $n$ th term of this progression is $-16$ , find the value of $n$ .

[2]

Find the common difference, $d$ .

[1]

Question 3

SL & HLPaper 1

A baker is arranging cupcakes in rows to form a triangular display. The number of cupcakes in each row forms an arithmetic sequence. The first row has $3$ cupcakes, the second row has $5$ cupcakes, the third row has $7$ cupcakes, and so on, increasing by $2$ cupcakes per row. The baker is interested in the total number of cupcakes in the odd-numbered rows.

Write down the number of cupcakes in the $1^{\text{st}}$ , $3^{\text{rd}}$ , and $5^{\text{th}}$ rows.

[1]

Determine a formula for the number of cupcakes in the $n$ th odd-numbered row.

[3]

Calculate the total number of cupcakes in the first $8$ odd-numbered rows of the display.

[3]

Question 4

SL & HLPaper 1

The first three terms of an arithmetic progression are $2w - 1$ , $5w - 2$ , and $6w - 1$ .

Show that $w = 1$ .

[2]

Determine an expression, in terms of $n$ , for the sum of the first $n$ terms of this arithmetic progression.

[3]

Show that the sum of the first $n$ terms can be expressed in the form $kn^2$ where $k$ is a constant. State the value of $k$ .

[1]

Question 5

SL & HLPaper 1

The first three terms of an arithmetic sequence are $k-1$ , $k+2$ , and $k^2-1$ .

Show that $k$ satisfies the equation $k^2 - k - 6 = 0$ .

[3]

Hence, find the possible values of $k$ and, for each value, state the common difference of the arithmetic sequence.

[4]

Question 6

SL & HLPaper 1

The first term of a progression is $2y$ and the second term is $y^2$ .

For the case where the progression is arithmetic with a common difference of $3$ , find the possible values of $y$ and the corresponding values of the third term.

[3]

Question 7

SLPaper 1

The $n$ th term of an arithmetic progression is given by $v_n = 15 - 3n$ .

State the value of the initial term, $v_1$ .

[1]

Given that the $n$ th term of this progression is $-33$ , find the value of $n$ .

[2]

Find the common difference, $d$ .

[2]

Question 8

SL & HLPaper 1

Sequences question.

The $n$ th term of a sequence is $5 - 3n$ .

Write down the 23rd term in this sequence.

[1]

The first five terms of another sequence are $5, 9, 13, 17, 21$ .

Write down an expression, in terms of $n$ , for the $n$ th term of this sequence.

[2]

Question 9

SLPaper 1

The first three terms of an arithmetic sequence are $v_1$ , $5v_1-8$ and $3v_1+8$ .

Show that $v_1=4$ .

[2]

Show that the sum of the first $n$ terms of this arithmetic sequence is a perfect square.

[4]

Question 10

SLPaper 1

Consider three integers $a$ , $b$ , $c$ which form a strictly increasing arithmetic sequence in that order.

Show that $b$ is the mean of $a$ and $c$ .

[2]

If $2b$ is the range, find the value of $a$ .

[2]

A student said that this forms a geometric sequence of common ratio 2. Is that correct? Explain why or why not.

[2]