What 2 numbers come next... 360, 180, 120, 90...?

Question

Please explain how you got the answer.

Answer 1

Here are 3 possibilities:

a) Series continues with 40, 45, 13 1/3, 22 1/2, ...

b) Series continues with 72, 60, 51.429, 45, ...

c) Series continues with 0, -240, -720, ...

How can that be ?

In fact it can be any two numbers you like, with sufficient

complexity to the rules.

Here are the three rules I used:

a) alternate between 1/3 and 1/2 of the number two back in the series:

360/3 = 120, 120/3 = 40

180/2 = 90, 90/2 = 45

b) Use successive ratios n/(n+1):

360 * 1/2 = 180

180 * 2/3 = 120

120 * 3/4 = 90

90 * 4/5 = 72

72 * 5/6 = 60

60 * 6/7 = 51.429

51.429 * 7/8 = 45

c) a[n] =  -15 x³ + 105 x² - 270 x + 360

a[0] = 360

a[1] = 180

a[2] = 120

a[3] = 90

a[4] = 0

a[5} = -240

a[6] = -720

All of those are *equally* valid, and that's just for starters.

.

Answer 2

Interesting

I believe that these are the degrees of a circle in descending order

So a full circle  or 1/1 * 360   = 360 degrees

Half a circle  or 1/2 * 360   = 180 degrees

A third of a circle or 1/3 * 360 = 120 degrees

A quarter of a circle or 1/4 * 360 = 90 degrees

So the next members of the series would be

A fifth of a circle  or 1/5 * 360 =  72  degrees

A sixth of a circle or 1/6 * 360 = 60 degrees

Answer 3

72 and 60

If you look at the sequence 180 is 1/2 of 360, 120 is 1/3 of 360, 90 is 1/4 of 360.  So continuing with that pattern 1/5  * 360 = 72 and 1/6 * 360 = 60

Answer 4

360

360(1/2) = 180

360(1/3) = 120

360(1/4) = 90

360(1/5) = 72

360(1/6) = 60