SL 1.3—Geometric sequences and series - IB Questionbank | RevisionDojo

SL 1.1—Using standard form

SL 1.2—Arithmetic sequences and series

SL 1.3—Geometric sequences and series

SL 1.4—Financial apps – compound interest, annual depreciation

SL 1.5—Intro to logs

SL 1.6—Simple proof

SL 1.7—Laws of exponents and logs

SL 1.8—Sum of infinite geo sequence

SL 1.9—Binomial theorem where n is an integer

AHL 1.10—Perms and combs, binomial with negative and fractional indices

AHL 1.11—Partial fractions

AHL 1.12—Complex numbers – Cartesian form and Argand diag

AHL 1.13—Polar and Euler form

AHL 1.14—Complex roots of polynomials, conjugate roots, De Moivre’s, powers & roots of complex numbers

AHL 1.15—Proof by induction, contradiction, counterexamples

AHL 1.16—Solution of systems of linear equations

SL 1.3—Geometric sequences and series Questionbank

Practice SL 1.3—Geometric 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

Find the $7^{th}$ term of the geometric progression $100, 50, 25, \dots$

[3]

Question 2

SL & HLPaper 1

The sum of the first $n$ terms of a geometric progression is given by the formula $S_n = 2^{n+1}-2$ , for $n \ge 1$ .

Find the first term of the progression.

[2]

Find the common ratio of the progression.

[3]

Find the $5^{th}$ term of the progression.

[2]

Question 3

SL & HLPaper 1

The product of the first three terms of a geometric progression is $216$ . The sum of the first three terms is $26$ .

Find the first term and the common ratio.

[7]

Question 4

SL & HLPaper 1

A geometric sequence has $u_3 = 36$ and $u_6 = -972$ .

Determine the second term of the sequence.

[5]

Question 5

SL & HLPaper 1

The third term of a geometric progression is $54$ and the sixth term is $-16$ .

Find the common ratio.

[3]

Find the first term.

[1]

Question 6

SL & HLPaper 1

The first term of an arithmetic progression is $8$ and the sum of the first $5$ terms is $70$ .

Find the common difference of the progression.

[2]

The first term, the fifth term and the $n^{th}$ term of this arithmetic progression are the first term, the second term and the third term respectively of a geometric progression.

Find the common ratio of the geometric progression and the value of $n$ .

[5]

Question 7

SL & HLPaper 1

In the expansion of $(p + qx)^5$ , where $p$ and $q$ are non-zero constants, the coefficients of $x$ , $x^2$ and $x^4$ are the first, second and third terms respectively of a geometric progression.

Find the value of $\frac{p}{q}$ .

[5]

Question 8

SL & HLPaper 1

Consider a geometric sequence where the first term $a_1 = 4\sin x$ and the second term $a_2 = \sin 4x$ , where $\sin x \neq 0$ .

Find the common ratio $r$ of this geometric sequence in terms of $\cos$

[4]

Given that $|r| \not= 1$ , explain why the sum to infinity exists and find it for $x=\frac{\pi}{6}$ giving your answer in the form $\frac{a+b\sqrt{c}}{d}$

[5]

Question 9

SL & HLPaper 1

Consider four integers $a$ , $b$ , $c$ , and $d$ such that $a<b<c<d$ .

Let $a<b<c<d$ where the maximum is twice the range, and the median is 10. Find the value of $a$ for which the mean is 11.

[4]

Let $a$ and $d$ be the same as your answers to part (a), but $b$ and $c$ have been altered. If $a,b,c,d$ create a geometric sequence, find the median.

[4]

Question 10

SLPaper 1

Liam baked a very large cherry pie that he cuts into slices to share with his friends. The smallest slice is cut first. The volume of each successive slice of pie forms a geometric sequence.

The second smallest slice has a volume of $30 \, \text{cm}^3$ . The fifth smallest slice has a volume of $240 \, \text{cm}^3$ .

Find the volume of the smallest slice of pie.

[2]

The cherry pie has a volume of $61\,425\,\text{cm}^3$ .

Find the total number of slices Liam can cut from this pie.

[2]

Paper

Level

Question 1

SL & HLPaper 1

Find the $7^{th}$ term of the geometric progression $100, 50, 25, \dots$

[3]

Question 2

SL & HLPaper 1

The sum of the first $n$ terms of a geometric progression is given by the formula $S_n = 2^{n+1}-2$ , for $n \ge 1$ .

Find the first term of the progression.

[2]

Find the common ratio of the progression.

[3]

Find the $5^{th}$ term of the progression.

[2]

Question 3

SL & HLPaper 1

The product of the first three terms of a geometric progression is $216$ . The sum of the first three terms is $26$ .

Find the first term and the common ratio.

[7]

Question 4

SL & HLPaper 1

A geometric sequence has $u_3 = 36$ and $u_6 = -972$ .

Determine the second term of the sequence.

[5]

Question 5

SL & HLPaper 1

The third term of a geometric progression is $54$ and the sixth term is $-16$ .

Find the common ratio.

[3]

Find the first term.

[1]

Question 6

SL & HLPaper 1

The first term of an arithmetic progression is $8$ and the sum of the first $5$ terms is $70$ .

Find the common difference of the progression.

[2]

The first term, the fifth term and the $n^{th}$ term of this arithmetic progression are the first term, the second term and the third term respectively of a geometric progression.

Find the common ratio of the geometric progression and the value of $n$ .

[5]

Question 7

SL & HLPaper 1

In the expansion of $(p + qx)^5$ , where $p$ and $q$ are non-zero constants, the coefficients of $x$ , $x^2$ and $x^4$ are the first, second and third terms respectively of a geometric progression.

Find the value of $\frac{p}{q}$ .

[5]

Question 8

SL & HLPaper 1

Consider a geometric sequence where the first term $a_1 = 4\sin x$ and the second term $a_2 = \sin 4x$ , where $\sin x \neq 0$ .

Find the common ratio $r$ of this geometric sequence in terms of $\cos$

[4]

Given that $|r| \not= 1$ , explain why the sum to infinity exists and find it for $x=\frac{\pi}{6}$ giving your answer in the form $\frac{a+b\sqrt{c}}{d}$

[5]

Question 9

SL & HLPaper 1

Consider four integers $a$ , $b$ , $c$ , and $d$ such that $a<b<c<d$ .

Let $a<b<c<d$ where the maximum is twice the range, and the median is 10. Find the value of $a$ for which the mean is 11.

[4]

Let $a$ and $d$ be the same as your answers to part (a), but $b$ and $c$ have been altered. If $a,b,c,d$ create a geometric sequence, find the median.

[4]

Question 10

SLPaper 1

Liam baked a very large cherry pie that he cuts into slices to share with his friends. The smallest slice is cut first. The volume of each successive slice of pie forms a geometric sequence.

The second smallest slice has a volume of $30 \, \text{cm}^3$ . The fifth smallest slice has a volume of $240 \, \text{cm}^3$ .

Find the volume of the smallest slice of pie.

[2]

The cherry pie has a volume of $61\,425\,\text{cm}^3$ .

Find the total number of slices Liam can cut from this pie.

[2]