# What is the next number? 1,2,8,48,384,?

• It’s 3840. The pattern is

multiply by 2 then 4 then 6 then 8 then 10, … .

• 1

1×2 = 2

2×4 = 8

8×6 = 48

48×8 = 384

384×10 = 3840

12×3480 = 41760

This can be written as either of the following:

(2n)!!

(2^n) n!

Note that !! does not mean to do factorial twice. The ! means factorial. !! means something called "double factorial."

So for n=5 (what you want), put:

(2^5) 5!

= 32 × (5 × 4 × 3 × 2 × 1)

= 32 × 120 = 3480

Double factorial is where you take every other one. For n=5, we can do:

(2×5)!! = 10!!

= 10 × 8 × 6 × 4 × 2

notice we take every other factor as we count down from 10

= 3480

Which also demonstrates how this recursion actually defines the !! function.

• 2 x 1 = 2

4 x 2 = 8

6 x 8 = 48

8 x 48 = 348

10 x 348 = 3480

12 x 3480 = 41,760

• 3840

1*2 = 2

2 *4 = 8

8 * 6 = 48

48 * 8 = 384

384 * 10 = 3840

thus multiply it times 10 to get 3840

• 1 2 8 48 384

• Appears to be successive multiples of 2, so 10 x 384 = 3840

• 3840…each subsequent number is being multipied by the next number counted by two.

1 (x2) 2 (x4) 8 (x6) 48 (x8) 384 (x10) 3840.

• 3840

You are multiplying each term by,then 4, then 6, then 8 then 10, then 12, etc

• 3840 followed by 46080

in statistics this is called (perfect) autocorrelation

try a harder one

• the sequence is like this!

1×2=2

2×4=8

8×6=48

48×8=384

so..

384×10=3840

hope this helped!