TMUA Series and Sequences
Like most College Entrance Exams, TMUA loves testing on series and sequences. So common are two types (Arithmetic and Geometric Progressions, and Binomial Expansions) that we have put them as standalone and separate topics. An ability to sum the first n numbers and n square numbers is essential as they are commonly tested as part of a bigger question. Limits are occasionally tested as part of sequences and series, however otherwise TMUA does not seem to test on limits - except for sums of infinite geometric series (see 'Arithmetic and Geometric Progressions'). Frequently, a series or sequence is defined by TMUA in a highly convoluted manner, and pattern finding techniques are required to establish the answer to the question.
For those so interested, we offer both one to one TMUA coaching on series and sequences, as well as online group coaching via Zoom - 'TMUA Binomial Expansions, Series and Sequences' is Session #15 of 20. Check our TMUA Group Coaching Schedule page for dates when these sessions are 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 series and sequences - 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 #57 - tests ability to sum first n+1 even numbers minus first n-1 odd numbers - Mild
- Teaser #178 - tests ability to find a pattern to simplify and sum a series of powers - Fairly Mild
- Teaser #102 - tests ability to simplify a sum of large powers of 2 - Standard
- Teaser #148 - tests evaluation of a limit of a sum of squares over a cube - Standard
- Teaser #136 - tests how to find the convergence value of a sequence - Standard
- Teaser #16 - tests ability to spot a series sum is a line of Pascals Triangle - Standard
- Teaser #148 - tests evaluation of a limit of a sum of squares over a cube - Standard
- Teaser #258 - tests a summation of numbers in various bases which simplifies to the sum of the first n numbers- Standard
- Teaser #233 - tests adding numbers in different bases by spotting a pattern - Standard
- Teaser #136 - tests how to find the convergence value of a sequence - Standard
- Teaser #442 - tests understanding of summing a series of logs to base less than one - Medium
- Teaser #37 - tests ability to sum a series of squares using difference of two squares trick - Medium
- Teaser #505 - tests ability to find the coefficient where powers of a and b are the same in a binomial expansion - Medium
- Teaser #240 - tests ability to spot pattern to find a(100) given a(1) and a(n) - Medium
- Teaser #484 - tests ability to use symmetry and patterns to sum a tricky looking trigonometric series - Medium
- Teaser #253 - tests knowledge of sums of n, n^2 and n^3 using some interesting relationships between them - Medium
- Teaser #86 - tests ability to solve a crossword puzzle of sequences - Quite Tough
- Teaser #279 - tests knowledge of a useful trick to find coefficient of x^3 in a binomial expansion - Quite Tough
TMUA Past Questions on Series and Sequences: SP p2 q16; 2016 p1 q4; 2016 p2 q6; 2017 p1 q11; 2017 p1 q17; 2017 p2 q6; 2018 p1 q8; 2018 p1 q20; 2018 p2 q7; 2019 p1 q3; 2019 p1 q4; 2019 p1 q19; 2020 p2 q15; 2021 p1 q13; 2021 p1 q15; 2022 p1 q5; 2022 p1 q11; 2022 p2 q2; 2023 p1 q4; 2023 p2 q16
Practice makes perfect - good luck in your studies!