What is the next number? 1,2,8,48,384,?
What is the next number in the sequence 1, 2, 8, 48, 384? Can you explain the pattern or rule governing this series?
10 Answers
Jan 06, 2025
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
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
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