# Deduce the next term in this sequence: m,n,a,z,l,o,b,y,k,p,c,x,j

This is the question :

m,n,a,z,l,o,b,y,k,p,c,x,j

In the letter series above, which one of the following choices logically follows

d

k

m

q

r

Thanks

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I have no idea if this is right, but: 2nd letter is n jump 4 get o jump 4 get p jump 4 get ... q ? – Thomas Apr 21 '12 at 20:28
Is this your math homework? – Rasmus Apr 21 '12 at 20:30
There are uncountably many sequences starting with those letters. This isn't mathematics, it's vague guesswork. – user5137 Apr 29 '12 at 5:43

There are four sequences here, one of which is suggested by @Thomas:

• m,l,k,j (alphabet counting backwards)
• n,o,p (this one will give you the next letter)
• a,b,c
• z,y,x
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Be careful! It need not be $q$. Recently I have seen this sequence: $m,n,a,z,l,o,b,y,k,p,c,x,j,j,j,j,j,j,j,...$ (and somewhere there followed some $x$, but unfortunately I do not remember the exact positions and how many of them were there in total).

To give an explanation: You have implicitly assumed that there is a rule that generates your sequence. Many mathematicians do that, and in your case it might even be correct. But in most cases it is wrong. A finite formula defines an infinite sequence. But an infinite sequence can never (that means "never" and not "at a certain time") define a finite formula.

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It's $q$. Look at the pairs of numbers. One sequence is going up and down from the middle $(m,n), (l,o) ,(k,p), (j,?)$ while the other is going down and up from the end $(a,z) , (b,y), (c,x)$.

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converting the series in numbers gives

$$13,14,1,26,12,15,2,25,11,16,3,24,10$$ $$13,14 ,,,,1,26,12,15,,,,,2,25,11,16,,,,,3,24,10$$ $$0,27,13,14 ,,,,1,26,12,15,,,,,2,25,11,16,,,,,3,24,10,X$$

its the series,

$$a,b,c,d,,,,(a+1),(b-1),(c-1),(d+1),,,,(a+2),(b-2),(c-2),(d+2),,,,(so-on)$$ The pattern is very obvious, X=17, i.e. the alphabet q

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After a little inspection it looks like there is a simple pattern. If you start with the first letter (m) and then count the next three letters (n, a, z) the fourth letter will either be letter (m-1 = l) or letter (m+1 = n) depending on what's in the three letter sequence (n, a, z in the first case).

Whichever letter is not in the three letter sequence, or has not appeared in the total sequence, will come next. So the next letter should be (q) or (p+1), since (p-1 = o) and that has already be used in the sequence.

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