4 self-marking IGCSE and Additional Maths practice questions on Recognising arithmetic and geometric progressions, written specifically for Cambridge IGCSE Additional Maths (0606), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Single and Extended tier. Instant marking with full worked solutions on every question.
Sample Recognising arithmetic and geometric progressions questions
A few of the 4 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 6
For the sequence 7,11,15,19,…:
(a) State whether it is an arithmetic progression (AP) or a geometric progression (GP). [1]
(b) State the common difference or common ratio, as appropriate. [1]
Show the worked solution
11−7=4
What are the common mistakes in Recognising arithmetic and geometric progressions?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Identifies which sequence is arithmetic vs geometric by comparing the size of the terms, instead of checking for a constant common difference or common ratio
Which sequence is which doesn't depend on the SIZE of the terms - check whether consecutive terms have a constant difference (Sequence A: +4 each time, an AP) or a constant ratio (Sequence B: ×3 each time, a GP).
Misidentifies a sequence with a constant additive difference (arithmetic) as having a constant multiplicative ratio (geometric), or vice versa
The terms increase by a FIXED AMOUNT each time (+4), not by a fixed multiplying factor - since consecutive terms have a common difference, this is an AP, not a GP.
Quick answers about Recognising arithmetic and geometric progressions
How many Recognising arithmetic and geometric progressions practice questions are there?
There are 4 self-marking IGCSE and Additional Maths Maths questions on Recognising arithmetic and geometric progressions, written for Cambridge IGCSE Additional Maths (0606), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Single and Extended tier. Each one is marked instantly and has a full worked solution.
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,
15−11=4
,
19−15=4
- the difference between consecutive terms is constant, so this is an arithmetic progression with common difference
4
.
Question 22 marksGrade 7
Sequence A is 6,10,14,18,…. Sequence B is 6,18,54,162,….
(a) State which sequence is an arithmetic progression. [1]
(b) State which sequence is a geometric progression. [1]
Show the worked solution
Sequence A: 10−6=4, 14−10=4, 18−14=4
Question 34 marksGrade 9
An arithmetic progression has first term 4 and non-zero common difference d. The 1st, 3rd, and 7th terms of the progression form the first three terms of a geometric progression.
Find the value of d. [4]
Accepts a solution to a factorised equation that is explicitly excluded by the question's given conditions, instead of rejecting it
The factorised equation 4d(d−2)=0 gives d=0 or d=2 - but d=0 makes every term of the AP identical, which the question explicitly excludes ("non-zero common difference"), so only d=2 is a valid answer.
- a constant difference, so Sequence A is an AP.
Sequence B: 618=3, 1854=3, 54162=3 - a constant ratio, so Sequence B is a GP.