Pattern Recognition - 169

Find out the next number in the series.

1,7,50 ,8, 5,39,11,6,157,13,10,69,14,12,_,................

Answer 

1, 7, 50 , 8,  5 , 39, 11, 6, 157, 13, 10, 69, 14, 12,_,................

50   =  1 * 1    +    7 * 7

39   =  8 * 8     -    5 * 5

157 =  11 * 11 +   6 * 6

69   =  13 * 13  -   10 * 10

Next number  14 * 14  + 12 * 12 = 340

1,7,50 ,8, 5,39,11,6,157,13,10,69,14,12,340,................

Pattern Recognition - 168

Find out the next two numbers in the series.

1 ,2 ,2 ,  3 , 4 , 12, 6 , 6 ,36 ,10 , 8,_ ,_

Answer

1 , 2 , 2  ,  3 ,  4 ,  12,  6 ,  6 , 36 , 10 , 8, _  ,_

1 , 3 , 6 , 10 , _ , _ , .............Triangular number series ; Next two numbers  15 ,21

2 , 4 , 6 , 8 , _ , _ ................ Even number series ; Next two numbers   10,12

2   = 1 * 2

12 = 3 * 4

36 = 6 * 6

Next two numbers   10 * 8 = 80  ,  15

1 ,2 ,2 ,  3 , 4 , 12, 6 , 6 ,36 ,10 , 8, 80 ,15, .......................

Pattern Recognition - 167

Find out the next number in the series.

1375  , 55 , 2786 , 102 , 3435 , 50 , 4265 , _ ,.........................

Answer

1375  , 55 , 2786 , 102 , 3435 , 50 , 4265 , _ ,.........................

55  =  (1 + 3 + 7 ) * 5  

102=  (2 + 7 + 8 ) * 6  

50  =  (3 + 4 + 3 ) * 5

Next number =  (4 + 2 + 6) * 5   = 60

1375  , 55 , 2786 , 102 , 3435 , 50 , 4265 , 60 ,.........................

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 , ............................