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(n-2)/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 n-sided 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 90-108-120 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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