Could you help me find the patterns in these numbers?? (Re- post)?

Question

3,5,11,29,83,245

3,-12,48,-192,768

1,5,14,30,55,91

1,2,5,14,41,122

0,3,8,15,24,35

Answer 1

Whenever I search for a pattern among a series of numbers, I start by looking at the differences between them...

[ 3, 5, 11, 29, 83, 245, ... ] -

Looking at the set of differences [ 2, 6, 18, 54, 162 ], you should notice that each term is three times the previous term:

[ 2 * 3 = 6 ]

[ 6 * 3 = 18 ]

[ 18 * 3 = 54 ]

[ 54 * 3 = 162 ]

[ 3, -12, 48, -192, 768 ] -

Looking at the set of differences [ -15, 60, -240, 960 ], you should notice that each term is minus four times the previous term:

[ -15 * -4 = 60 ]

[ 60 * -4 = -240 ]

[ -240 * -4 = 960 ]

[ 1, 5, 14, 30, 55, 91 ] -

Looking at the set of differences [ 4, 9, 16, 25, 36 ], you should notice that each term is a square:

[ 2 * 2 = 4 ]

[ 3 * 3 = 9 ]

[ 4 * 4 = 16 ]

[ 1, 2, 5, 14, 41, 122 ] -

Looking at the set of differences [ 1, 3, 9, 27, 81 ], you should notice that each term is three times the last term.

[ 0, 3, 8, 15, 24, 35 ] -

Looking at the set of differences [ 3, 5, 7, 9, 11 ], you should notice that each term is two more than the last term.