what are the missing numbers and landmarks for the set of numbers:48,50,51,51,57,59,60,63,69,_,76,_?
To find the missing numbers in the set, we need to observe the pattern and identify the rule by which the numbers are increasing.
Looking at the given numbers: 48, 50, 51, 51, 57, 59, 60, 63, 69, __, 76, __
Let's analyze the differences between the consecutive numbers:
50 - 48 = 2
51 - 50 = 1
51 - 51 = 0
57 - 51 = 6
59 - 57 = 2
60 - 59 = 1
63 - 60 = 2
69 - 63 = 6
__ - 69 = ?
76 - __ = ?
From the given differences, we can observe that there is an alternating pattern. The differences are alternating between 2 and 1. This indicates that the numbers are increasing by 2, then by 1, repeating this pattern.
Now, let's apply this pattern to find the missing numbers:
Starting from 69 and increasing by 2, we find the next number:
69 + 2 = 71
Next, increasing by 1, we find the next number:
71 + 1 = 72
Therefore, the missing numbers in the set are 71 and 72.
Hence, the complete set of numbers, including the missing ones and landmarks, is:
48, 50, 51, 51, 57, 59, 60, 63, 69, 71, 72, 76.