There are infinitely many polynomials of order 5 that will give these as the first five numbers and any one of these could be "the" rule. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
A rule, based on a polynomial of order 4 is:U(n) = (35n^4 - 394n^3 + 1555n^2 - 2420n + 1284)/4 for n = 1, 2, 3, ...
174 =============== 18 = 15+3 54 = 18x3 57 = 54+3 171= 57x3 174= 171+3
The next number could be 26 The next number could be 12 - - - - - - - - - The next number that is in the sequence is 12.
6 12 9 18 15 30 27 54 51
the next two are 174 and 522.
The pattern is add three and then multiply by three. The next number is 174.
174 =============== 18 = 15+3 54 = 18x3 57 = 54+3 171= 57x3 174= 171+3
The 18th triangular number is calculated using the formula ( T_n = \frac{n(n + 1)}{2} ), where ( n ) is the position in the sequence. For ( n = 18 ), this gives ( T_{18} = \frac{18 \times 19}{2} = 171 ). Therefore, the 18th triangular number is 171.
The next number could be 26 The next number could be 12 - - - - - - - - - The next number that is in the sequence is 12.
2 + 171=173 1 + 7 + 3 = 11 < 18
18
The next number in the sequence would be 25.
6 12 9 18 15 30 27 54 51
22
the next two are 174 and 522.
The pattern is add three and then multiply by three. The next number is 174.
The pattern in the series appears to alternate between adding 3 and multiplying by 3. Starting with 15, we add 3 to get 18, then multiply by 3 to get 54. Next, we add 3 to 54 to get 57, and then multiply by 3 to reach 171. Following this pattern, the next step is to add 3 to 171, which gives us 174. Thus, the next number in the series is 174.
The final number in this sum would be 18: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 = 171