A pattern in a puzzling sequence

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Question from Martha, a teacher:

A1 2 3 B 5 6 7 C 9 10 11 D 13 14 15

USE THIS PATTERN SUGGESTED TO HELP YOU FIND
THE MISSING TERMS IN THE PROBLEM BELOW:
a) H _ _ _ b) R _ _ _
c) _ _ 50 _ d) _ _ _ 63
e) _ @#$ where @ + # + $ = 258

Hello Martha,
Notice that all the letters correspond to numbers which are multiples of 4.

A	B	C	D	E	F	G	H	I	Etc...
0	4	8	12	16	20	24	28	32	Etc...

This means that the number which corresponds to the n^th letter of the alphabet is given by 4(n - 1).

‘A’ is the first letter, thus its number is 4(1 - 1) = 4(0) = 0.

‘F’ is the sixth letter, and its number is 4(6 - 1) = 4(5) = 20.

This should help you with parts a)-d). Part e) requires slightly more work.

We must determine which letter fills in _@#$ where @ + # + $ = 258.

Well @,#,and $ are consecutive numbers, so # = @ + 1 and $ = @ + 2. Thus 3@ + 3 = 258 and we can solve for @, bringing us back to a situation like in parts c) or d).

Tyler

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.