TMUA Arithmetic and Geometric Progressions
TMUA likes questions on both of these progression types and a question on this topic appears in the exam most years. It tends to be either a 'direct' arithmetic or geometric progression question (where you are given some information and then required to calculate missing elements such as common ratio, first term, nth term or sum to infinity), or an indirect arithmetic or geometric progression question, where first recognising and then manipulating the progression is usually the final part of a seemingly unrelated question.
For those so interested, we offer both one to one TMUA coaching on arithmetic and geometric progressions, as well as online group coaching via Zoom - 'TMUA Arithmetic and Geometric Progressions' is Session #14 of 20. Check our TMUA Group Coaching Schedule page for dates when this session is available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our 'Online Coaching FAQ'.
Feel free to contact us if you require more information regarding any of the above.
Free Revision Resources
The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions on arithmetic and geometric progressions - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.
- Teaser #289 - tests ability to find a geometric series given clues - Fairly Mild
- Teaser #396 - tests how to sum a geometric series to infinity, though with a small twist - Standard
- Teaser #463 - tests how to find the number of terms in an arithmetic sequence given certain criteria - Standard
- Teaser #346 - tests knowledge of nth term and sum of an arithmetic progression to answer a ratio question- Standard
- Teaser #483 - tests ability to discover which of five options is the only possible first term of an arithmetic progression - Standard
- Teaser #53 - tests how to sum a hidden geometric series - Standard
- Teaser #325 - tests knowledge of a) recognising and b) summing an arithmetic/geometric series - Medium
- Teaser 312 - tests how to find common terms in three different arithmetic series - Medium
- Teaser #299 - tests knowledge of a) recognising and b) summing an arithmetic/geometric series - Medium
- Teaser #111 - tests finding 3rd term given xth term and sum of first x terms is the same - Medium
- Teaser #91 - tests how to find number of terms of Arithmetic Progression given other clues - Medium
- Teaser #321 - tests how to find ratio of a geometric series when there is a relationship between even terms (ie 2nd, 4th..) and odd terms (ie 1st, 3rd...) - Medium
- Teaser #284 - tests knowledge that arithmetic mean >= geometric mean to find a minimum of a complex trig expression - Quite Tough
[Note: We also have an 'Arithmetic and Geometric Series' playlist on our YouTube channel however the videos in this playlist are not all relevant to TMUA (some are too easy, some are too hard, and many cover topics not tested in TMUA).]
TMUA Past Questions on Arithmetic and Geometric Progressions: SP p1 q19; 2016 p1 q14; 2016 p2 q6; 2016 p2 q12; 2017 p1 q7; 2017 p2 q3; 2018 p1 q2; 2018 p1 q8; 2018 p1 q20; 2018 p2 q7; 2018 p2 q16; 2019 p1 q5; 2019 p2 q11; 2020 p1 q4; 2020 p2 q14; 2021 p1 q3; 2022 p1 q8; 2022 p1 q11; 2022 p2 q8; 2023 p1 q4; 2023 p1 q17; 2023 p1 q18; 2023 p2 q9; 2023 p2 q15; 2023 p2 q17
Practice makes perfect - good luck in your studies!