# What words come next in the sequence?

Try to figure out the next five words in the sequence.

Alpha, superb, succumb, economic, signed, shelf, corgi, within, improv, origami

Good luck!

Hint:

It might be worth it to take a look at the last letters of each word...

• Just to test out a theory: Are you sure 'crosswalk' is correct, rather than - say - 'corgi'? Thanks.
– Stiv
Commented Mar 17, 2023 at 17:00
• @Stiv Yes, it looks like I made a mistake. Thank you for pointing that out to me. Commented Mar 17, 2023 at 18:27

Here's a suggestion (explaining my earlier comment on the question itself). If you look...

...at the last letters of the words, with a little further processing they form a recognisable sequence.

A, B, B, C, D, F, I, N, V, I...

If you convert these to numbers based off their position in the English alphabet (i.e. using 'A1Z26'), we get:

1, 2, 2, 3, 4, 6, 9, 14, 22, 9, ...

Now subtract 1 from each number to end up with:

0, 1, 1, 2, 3, 5, 8, 13, 21, 8, ...

Oh look, the first 9 terms here are the beginning of the Fibonacci sequence! (i.e. Each term after the initial '0' and '1' is found by adding the previous 2 terms together...) What's with the '8' at the end? Well, add 26 (the number of letters in the English alphabet) to this and we get 34, the next term...

So it seems we have a rule, and we should be able to apply it to find candidates for the next few terms by...

...finding the A1Z26 letters that correspond to the next terms in the Fibonacci sequence modulo 26 with 1 added (or just the A0Z25 letters without adding that 1 at the end).

This means the next five terms should...

...end with the letters D, L, O, Z, and N:

55 mod 26 = 3, add 1 to get 4 which is equivalent to D;
89 mod 26 = 11, add 1 to get 12 which is equivalent to L;
144 mod 26 = 14, add 1 to get 15 which is equivalent to O;
233 mod 26 = 25, add 1 to get 26 which is equivalent to Z;
377 mod 26 = 13, add 1 to get 14 which is equivalent to N.

This is the only rule I can spot amidst the words - there doesn't seem to be any pattern to the first letters (which appear to spell ASSESS CWIO, which doesn't seem to have a relevant meaning), the number of letters in the words, or particular letters that feature at other positions, so really any words that satisfy the rule found above should do. I therefore suggest:

ACI(D), META(L), DISC(O), JAZ(Z) and FUSIO(N).