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 nth term of an arithmetic progression is given by $n^{th} \text{ term} = 24 - 2n$

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

[1]

Given that the nth 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 $(1^{st})$ , $(3^{rd})$ , and $(5^{th})$ 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 progression 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 progression.

[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

SL & HLPaper 1

The nth term of a sequence is $5 – 3n$ . Write down the 23rd term in this sequence.

[1]

The first five terms of another sequence are

$5 \quad 9 \quad 13 \quad 17 \quad 21$

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

[2]

Question 8

SLPaper 1

The nth 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 nth term of this progression is -33, find the value of n.

[2]

Find the common difference, $d$ .

[2]

Question 9

SLPaper 1

The initial trio of terms in an arithmetic progression are $v_1$ , $5v_1-8$ and $3v_1+8$ .

Demonstrate that $v_1=4$ .

[2]

Establish that the total of the first $n$ terms of this arithmetic progression is a perfect square.

[4]

Question 10

SLPaper 1

Consider three integers $a$ , $b$ , $c$ which follow an arithmetic sequence respectively.

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

[2]

if $2b$ is the range, find $a$

[2]

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

[2]