If a number sequence begins $1, 3, 4, 6, 7, 9, 10, 12 . . .$ , which of the following numbers does NOT appear in the sequence?

34

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43

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57

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65

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72

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Solution

The correct option is E $65$
$1, 3, 4, 6, 7, 9, 10, 12...$
$= (1, 4, 7, 10...), (3, 6, 9, 12...)$
If a number can be written in the form of $(3 k)$ or $(3 k + 1)$ ., then it will appear in the sequence.
Now check options
For $34 = 3 (11) + 1 = 3 k + 1$ , where $k = 11$
For $43 = 3 (14) + 1 = 3 k + 1$ , where $k = 14$
For $57 = 3 (19) = 3 k$ , where $k = 19$
For $72 = 3 (24)$ , where $k = 24$
For Here $65 = 3 (21) + 2 = 3 k + 2$
$(3 k + 2)$ will not appear.
Therefore, $65$ will not appear in the sequence.

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If a number sequence begins 1,3,4,6,7,9,10,12..., which of the following numbers does NOT appear in the sequence?

If a number sequence begins $1, 3, 4, 6, 7, 9, 10, 12 . . .$ , which of the following numbers does NOT appear in the sequence?