Brain Teasers and Puzzles 

Workings

Hint
The sequence involves both adding and multiplying in some way.

Answer
153.

The sequence is created using: +1 x1 +2 x2 +3 x3 +4 x4 +5.

Workings

Hint
The words begin with the letters R, S, T.

Answer
RADII, SKIING, TAXIING.

You could also have GENII.

Workings

Hint
Calendar.

Answer
Dragon.

From the Chinese calendar in reverse order.

Workings

Hint
Try writing the numbers out as letters.

Answer
45.

Reasoning
Each term increases by the number of letters in the previous term (ignoring any hyphens).
1  + length("ONE")       = 4
4  + length("FOUR")      = 8
8  + length("EIGHT")     = 13
13 + length("THIRTEEN")  = 21
21 + length("TWENTYONE") = 30
30 + length("THIRTY")    = 36
36 + length("THIRTYSIX") = 45