With U{n} = (4n⁵ - 57n⁴ + 306n³ - 759n² + 890n - 336)/24
U{1, ..., 5} = {2, 3, 5, 7, 11}
U{6} = 42
However, I think the rule your teacher wants you to give is it is a list of the prime numbers, so it continues: 13, 17, 19, 23, 29, ...
The pattern will be +2, +3, +4, +4
prime numbers
If you mean: 2 5 11 23 47 then they are increasing by 3 6 12 24
Add 3 each time
The pattern rule for the given sequence is: starting with 0, add 3, then subtract 1, then add 2, then add 2, then add 3, then add 1, and the pattern repeats. This can be written as: +3, -1, +2, +2, +3, +1. This rule can be used to predict the next numbers in the sequence.
The pattern will be +2, +3, +4, +4
prime numbers
Everytime you move to the next number you add 1, then 2, then 3, etc.1+1=22+2=44+3=77+4=1111+5=1616+6=2222+7=2929+8=37
It is: 3 6 12 24 48 .... double up each time
If you mean: 2 5 11 23 47 then they are increasing by 3 6 12 24
+2, +3, +2
There are many possibilities. One is: Un = (8n3 - 39n2 + 79n - 36)/6 for n = 1, 2, 3, ...
Add 3 each time
The difference doubles each time. 2+3=5.. 5+6=11.. 11+12=23..Therefore the next number in the sequence would be 47, since 23+24 = 47.
It is not a rule as such; those number are the first 10 prime numbers.
The rule for the pattern is y=x+2. That rule is in the table format in which it would originally be in, but the worded rule would be 'It increases by 2 each time'.
Starting with the number 4, applying the rule of multiplying by 2 and then subtracting 3 gives the following sequence: 4, 5, 7, 11, 19, 35. This pattern can be calculated as follows: 4 x 2 - 3 = 5, 5 x 2 - 3 = 7, 7 x 2 - 3 = 11, 11 x 2 - 3 = 19, 19 x 2 - 3 = 35.