Complete the pattern........
Number Theory
Level
pending
Fill in the next column of the table.- 1 I 3 I 9 I 3 I11 I18I13 I19 I 27 I 55 I.............. 2 I 6 I 2 I 7 I15I 8 I 17I 24I 34 I 29 I.......... 3 I 1 I 5 I12I 5 I13I 21I 21I 23 I 30 I..........
Hint- arrange the three series in a table by row
00 ,01,11
41 ;44, 56
51 , 45 , 40
31 , 33 , 89
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1 solution
Trying to figure out this table one row at a time is pretty maddening. The values increase, decrease, repeat, etc. , with no apparent pattern. But who said that the patterns had to be in rows? If you use peripheral vision to scan the table as a whole you will notice some familiar numbers. For example, there are lots of multiples of three. In fact, the first few multiples of three, in order, are hidden in the table. 1 3 9 3 11 18 13 19 27 55 2 6 2 7 15 8 17 24 34 29 3 1 5 12 5 13 21 21 23 30 And once we see that the patterns are diagonal, it is easy to spot another sequence, the primes! 1 3 9 3 11 18 13 19 27 55 2 6 2 7 15 8 17 24 34 29 3 1 5 12 5 13 2 1 2 1 23 30 The sequence that is left over is, of course, the Fibonacci numbers So the next column of the table is 3 1, 3 3, 89.