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
Add 5 to form the next number in the sequence, then subtract 2 . . . repeat. 0 + 5 = 5 5 - 2 = 3 3 + 5 = 8 8 - 2 = 6 . . . and the series continues :- 6 + 5 = 11 11 - 2 = 9 . . . and so on
The pattern will be +2, +3, +4, +4
prime numbers
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
There are many possibilities. One is: Un = (8n3 - 39n2 + 79n - 36)/6 for n = 1, 2, 3, ...
+2, +3, +2
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.
With each new term, you add a number n. This number is always odd, and increases by 2 with each term. So, starting with the first term, 2, you add n = 1 to get 3; add 3 to n = 3 to get 6; add 6 to 5 to get 11; and 7 to 11 to get 18. Here is the pattern written out: 2 + 1 = 3 3 + 3 = 6 6 + 5 = 11 11 + 7 = 18 ...
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'.
-31. The rule is t(n) = -2n3 + 12n2 -19n + 14 where n = 1, 2, 3, ...