Fill in the blanks:

2, 2.5, _, 4.25, 5.6, _, _, 9.625, 11.111..., 12.9, ...

If you convert all the decimals to fractaions, you get

2/1, 5/2, __, 17/4, 28/5, __, __, 77/8, 100/9, and 129/10

Notice the denominator is increasing by 1 in every term.

So, the missing terms must be ?/3, ?/6, and ?/7.

Check out the differences between the given numerators.

5-2 = 3

28 - 17 = 11

100 - 77 = 23

129 - 100 = 29

You start thinking prime numbers and biggety bam! If you increase each numerator by the next succesive prime number, starting with 3, you get your sequence.  Check it,

2 + 3 = 5, hence 5/2

5 + 5 = 10, therefore the missing term is 10/3 or 3.33...

10 + 7 = 17, hence 17/4

17 + 11 = 28. hence 28/5

28 + 13 = 41, therefore the missing term is 41/6 or 6.833...

41 + 17 = 58, therefore the last missing term is 58/7 or 8.28571428...

58 + 19 = 77, hence 77/8

77 + 23 = 100, hence 100/9 and finally

100 + 29 = 129, hence 129/10.

Tizight.

 

Posted by Marc on 2005-06-03 18:52:23