# Find the number sequence, which number come next?

8 0 9 24 10 120 11 336 12 __ ?

Hint:

It is logical.

720

Reason:

The first even term is 24*0, second is 24*1, third is 24*5, fourth is 24*14, and lastly we have 24*30. So we have 0, 1, 5, 14, 30. The difference between these numbers are the first 4 squares; 1², 2², 3², 4².

• [24, 120, 336, 720] all of them are completely divisible by [2,3,4,6,8,12,24]..
– user64002
Commented Nov 24, 2019 at 9:42

Is the answer 720 because there is an alternating pattern- the pattern of the even terms is like so +(6x4), +(6+18)x4), +(6+18+30)x4), +(6+18+30+42)x4) A pattern of 18,30,42 which is +12,+12

• Well? Is it right?
– PDT
Commented Nov 23, 2019 at 22:17

Good to have a different way of answering. My logic is little bit easy:

8 $$\hspace{2cm}$$9$$\hspace{2cm}$$10$$\hspace{2cm}$$11$$\hspace{2cm}$$12

$$\hspace{1cm}$$0 $$\hspace{2cm}$$24$$\hspace{2cm}$$120$$\hspace{2cm}$$336$$\hspace{2cm}$$___?

$$\hspace{0.4cm}1^3-1\hspace{1cm}$$ $$3^3-3$$ $$\hspace{1.2cm}$$ $$5^3-5$$ $$\hspace{1cm}$$ $$7^3-7$$ $$\hspace{1.2cm}$$ $$9^3-9$$

Next term is:

$$9^3-9 = 720$$

Somebody has already solved it, but here is the detail explanation again:

8           9           10          11         12

0             24         120         336

24 * 0        24 * 1     24 * 5      24 * 14

0             1          5           14

1          4           9

1^2        2^2         3^2      ->   4^2

1     +    4     +     9      +      16    =   30

Result:  24 * 30 = 720


another (and one of the shortest) reasoning for 720: the even terms are the square pyramidal numbers multiplied by 24.