Pattern Recognition -166

Find out the next two numbers in the series.

1216 , 1442 , 2884 , 56168, _ ,_ ,............

Answer

There is a small issue with the question. The first number doesn't fit to the pattern exactly.  

Anyways this is the pattern I had on mind.

12 16 ,   1442 ,    2884 ,   56168,   _   ,  _  ,............

14 = (12 +16)/2    42  =14 * 3

28 = (14+42)/2     84  =28 * 3

56= (28+84)/2      168= 56* 3

14 , 28 , 56 ,112 ,224 ,.......................

42 , 84 ,168 ,336,672,.....................

Next two numbers  112336 , 224672 

1216 , 1442 , 2884 , 56168,  112336 ,224672 ,............

Pattern Recognition - 165

Find out the next two numbers in the series.
3, 11, 85, 1029, _ , _ , .............................

Answer

3,   11,   85,   1028  , _ , _ , .............................

Tn =n^(n+1) + (n+1)

T1 = 1 ^ 2    + (1+1)

T2 = 2 ^ 3    + (2+1)

T3 = 3 ^ 4    + (3+1)

T4 = 4 ^ 5    + (4+1)

Next two numbers  

T5 = 5 ^ 6    + (5+1)   = 15625 +6   =15631

T6 = 6 ^ 7    + (6+1)   = 279936 + 7 = 279943

3,   11,   85,   1028  , 15631, 279943 , .............................

Pattern Recognition -164

Find out the next two numbers in the series.

132 , 119, 108 , 98 ,_, _, .....

Answer

132 ,   119,   108 ,   98 ,_, _, .....

119 =132 - 13

108 =119 - 11

  98 =108 - 10

Next two numbers   98 - 9 = 89   89 - 8 =81

132 , 119, 108 , 98 , 89 , 81, .....

Pattern Recognition - 163

Find out the next two numbers in the series.
2 ,  5 ,   18 ,  87 , _ , _ , ............................

Answer

2 ,  5 ,   18 ,  87 , _ , _ , ............................

Tn  = [Tn-1 * (n+1)]  - (n-1)

T2  = [T1 * (2+1)]  - (2-1) = 2 * 3  -1 = 5

T3  = [T2 * (3+1)]  - (3-1) = 5 * 4  -2 = 18

T4  = [T3 * (4+1)]  - (4-1) = 18 * 5  -3 = 87

T5  = [T4 * (5+1)]  - (5-1) = 87 * 6  -4 = 518

T6  = [T3 * (6+1)]  - (6-1) = 518 * 7 -5 = 3621

2 ,  5 ,   18 ,  87 ,  518 ,  3621 , ............................