78.
Fit the quartic polynomial
t(n) = (7n4 - 66n3 + 221n2 - 186n + 216)/24 for n = 1, 2, 3, ...
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6 is.
24, they are going up in 3's, 13, 16, 19 and 18, 21 so next number is 24.
Every next number is increased by 5. The next number in the sequence is 23.
18
To determine the pattern in the series 13, 18, 16, 21, 19, we can observe that there are alternating increases and decreases by 5 and 3, respectively. Starting with 13, we add 5 to get 18, then subtract 2 to get 16, add 5 to get 21, and finally subtract 2 to get 19. Following this pattern, the next number would involve adding 5 to 19, resulting in 24.