46, 51, 57, 64
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What numbers would you like to be missing?
Whatever numbers you specify, I can give you a formula for the general term of the pattern so that the numbers already specified, and the wanted numbers appear for the terms 1, 2, ..., n
However, the pattern given looks like it is: 36, 37, 39, 42, w, x, y, z, 72, 81, 91, 102, for which the simplest formula for the general term is t{n} = (x² -x + 72)/2 which means the missing terms t{5-8} are:
w = t5 = (5² - 5 + 72)/2 = 46
x = t6 = (6² - 6 + 72)/2 = 51
y = t7 = (7² - 7 + 72)/2 = 57
z = t8 = (8² -8 + 72)/2 = 64
The formula is derived from the fact that the difference between one term and the next is one more than the difference between the previous term and that term:
t2 = t1 + 1
t3 = t2 + 2 = t2 + 1 + 1
t4 = t2 + 3 = t2 + 2 + 1
→ t5 = t4 + 3 + 1 = t4 + 4 = 42 + 4 = 46
→ t6 = t5 + 4 + 1 = t5 + 5 = 46 + 5 = 51
→ t7 = t6 + 5 + 1 = t6 + 6 = 51 + 6 = 57
→ t8 = t7 + 6 + 1 = t7 + 7 = 57 + 7 = 64
→ t9 = t8 + 7 + 1 = t8 + 8 = 64 + 8 = 72
and the sequence continues.
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