What numbers are missing from this pattern 36 37 39 42 72 81 91 102?

Answer 1

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.

Answer 2

There is no information on how many numbers are missing and where, in the pattern they should have been. In the circumstances, the easiest answer is that the missing numbers are38, 40, 41, 43 to 71, 73 to 80, 82 to 90 and 92 to 101 in the pattern that comprises all integers from 36 to 102.