The sequence consists of triangular numbers, which can be calculated using the formula ( T_n = \frac{n(n + 1)}{2} ). The numbers in the sequence correspond to ( T_1, T_3, T_5, T_6, T_7, T_8, T_9 ) respectively. Following this pattern, the next number is ( T_{10} = \frac{10(10 + 1)}{2} = 55 ). Therefore, the next number in the sequence is 72.
20
3, -6, 12, 4, 20, ?
56
10 The sequence is given by xn = 60/n
The given pattern appears to alternate between two sequences: one sequence that doubles the previous number (3 to 6 to 12) and another that adds 1 to the previous number (4 to 20). Following this pattern, after 20, the next number in the doubling sequence would be 24, as it continues from 12. Thus, the next number in the pattern is 24.
25 is the next number that appears in that sequence.
20
20
3, -6, 12, 4, 20, ?
56
next in the sequence: 10,20,30,20
10 The sequence is given by xn = 60/n
16
Those are the factors of the number 60, in descending order. The next factor is 10.
22
The next number in the sequence will be 56.
20