Find a pattern fot this sequence. Usde the pattern to show the next two terms.
1,2,6,24,120,___,___?
1 * 2 = 2
2 * 3 = 6
6 * 4 = 24
24 * 5 = 120
120 * ? = ?
2/1 =?
6/2=?
24/6=?
120/24=?
see the pattern?
720
To find the pattern in the given sequence, we can look for the relationship between each term. Let's examine the differences between consecutive terms:
2 - 1 = 1
6 - 2 = 4
24 - 6 = 18
120 - 24 = 96
The differences don't seem to follow a constant pattern. However, if we consider the differences of the differences:
4 - 1 = 3
18 - 4 = 14
96 - 18 = 78
Now we see a pattern emerging. The differences of the differences are increasing by 11 each time. This suggests that the original sequence might be a sequence of factorials.
Let's check if the premise holds:
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
Indeed, the given sequence matches the pattern of factorials up to this point. Therefore, to find the next term, we calculate the factorial of 6:
6! = 720
Now, let's find the next term by adding the next difference:
78 + 11 = 89
Hence, the next two terms in the sequence are 720 and 89.