Can anyone help me figure out these patterns?

Question

My friend gave me some brain teasers, you have to find the pattern in both of these problems.

1) 0, 4, 8, 21, 52, 65
2) 15, 26, 40, 16, 37, 58

I worked all day on these problems and feel rather confused :(
I would appreciate any help.

Answer 1

Well the 1st one is add 4 and then reverse the digits. So 8+4=12 = 21reversed. 21=4 = 25 = 52 reversed. 52+4 = 56 = 65 reversed. 65+4 = 69 =96 reversed, etc

Answer 2

q1
0=0*1
4=1*4
8=2*4
21=3*7
52=4*13
65=5*13

answer=(n-1)*{3(2^x) + 1}
n=the nth # in series
x=0, 1, 2, 3...(increase if n-1 is odd, coz value in {..} always odd except when x=0, and {..} is even, then x increase when n-1 is even)

or maybe the 2nd no. is just 2x-1, making the term
=(n-1)[2x-1] if both number in previous term (in (..) and [..]) are even/even pair or odd/odd pair, and (n-1)x if both in previous term are of different (oddity?).

anyway the next term is always 150=6*25

q2
15[+11]26[+14]40[-24]16[+21]37[+21]58

dont know
no apparent similarity.

Answer 3

Maybe your friend is just playing a joke on you and there is no pattern.