A Regular Series
Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.
What number comes next in this series? The decimals are rounded to 4 places.
60, 90, 108, 120, 128.5714, 135, 140, 144, 147.2727, ?
Bonus
What do these numbers represent?
HintTry this angle: divide each number by 180.
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Answer
The next number is 150.
The formula is 180(n2)/n, starting with n=3 for the first term.
180*1/3=60
180*2/4=90
180*3/5=108
180*4/6=120
...
180*10/12=150
Bonus
These numbers are the size (in degrees) of the interior angles in a regular nsided polygon. An equilateral triangle has three 60 degree angles, a square has four 90 degree angles, a regular pentagon has five 108 degree angles, and so on. A regular dodecagon has twelve 150 degree angles.
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Comments
jazzmusician46
May 14, 2006
 wow...tough one! Thanks. 
blagh
May 14, 2006
 Not too tough, but wouldn't have thought about the bonus at all. Obvious when you mention it though. 
brainster
May 15, 2006
 Nice one! Really fresh view on the series for a change! 
mercenary007
May 15, 2006
 it was obvious... I got both the series and also the bonus answer 
RRAMMOHAN
May 23, 2006
 Got this one! Not an easy one though, but possible to solve if one has a mathematical bent of mind! 
lessthanjake789
Aug 29, 2006
 Didn't get it, but was ont he right track, and I noticed the curious interior angles, as 108 for whatever jumped out, but I didn't put it all together. Nicely done 
javaguru
Dec 24, 2008
 Cool teaser.
Surprised at how quickly I got it...something about 90108120 just clicked. 
omas
Dec 14, 2009
 Nice teaser!
I got it as soon as I saw the hint. All those memory from the high school came back to me! I really enjoyed. Thanks. 
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