A collection of sequences and some tips on how to identify them.
Below we go through some "learnable" sequences. If you just want some trivia ones for fun, check out The Online Encyclopedia of Integer Sequencess.
A common "harder" sequence is something like
- 12, 29, 63, 131 (x_n = 2x_{n-1}+5)
- 75, 41, 27, 20 (subtract by 34/2^n, next number should be 16.5)
Try to look out for:
- Do the numbers look special themselves? (powers, squares)
- Differences between numbers
- Dependence of future numbers on numbers prior
- The "length" of the repeating subsequences
- The general trend of the size of numbers
- 1, 1, 2, 3, 5, 8, 13, (Fibonacci)
- 1, 2, 4, 8, 16 (2^n)
- 1, 6, 21, 66 (3x_{n-1}+3)
These can be a little more challenging since they rely on your language skills a bit. Memorizing some of these sequences should help you a long way though.
Also a lot of tests try to make these sequences harder by starting in the middle of them.
So for example, if we had the months, then they would start like J, J, A, S, O so it's
less obvious.
- A, C, E, G (skip a letter in the alphabet)
- P, Q, S, T, V (two consecutive letters, then skip one)
- F, S, T, F, F, S, S, E, N, T (1st, 2nd, 3rd, ...)
- O, T, T, F, F, S, S, E (one, two, three, four, ...)
- M, V, E, M, J, S, U, N, P (Mercury, Venus, Earth, Mars, ...)
- M, T, W, T, F, S, S (Monday, Tuesday, Wednesday...)
- J, F, M, A, M, J (January, February, March, April)