What should come in place of question mark (?) in the following number series? 38, 195, ?, 4905, 24530, 122655

Correct Answer: 36

Explanation:

The given number series is 90 72 56 42 36 20

9 x 10 = 90

8 x 9 = 72

7 x 8 = 56

6 x 7 = 42

5 x 6 = 30 (not 36) 

4 x 5 = 20

 

Hence, the odd man in the given number series is 36.

Correct Answer: 450.187

Explanation:

Pattern is

• 3

• 3 x 3.5 = 10.5

• 10.5 x 3.5 = 36.75

• 36.75 x 3.5 = 128.625

• 128.625 x 3.5 = 450.187

Correct Answer: 47

Explanation:

The next number in the series is

143 143 136 110

      0    7      26 (Differences)

  $$\begin{gathered} 1 3 - 1 , 2 3 - 1 , 3 3 - 1 , 4 3 - 1 , . . . \\ Now the next number is given by \\ 110 - ( 4 3 - 1 ) = 110 - 63 = 47 . \end{gathered}$$

Correct Answer: 156

Explanation:

Here the given series 7  18  42  94  204 follows a pattern that, 

7

7 ×2+4 = 18

18 ×2+6 = 42

42 ×2+10 = 94

94 ×2+16 = 204

Similarly,

4

4 ×2+4 = 12

12 ×2+6 = 30

30 ×2+10 = 70

70 ×2+16 = 156

Hence, the value of P = 156.

Correct Answer: 1962

Explanation:

Arithmetic Series ::

 

An Arithmetic Series is a series of numbers in which each term increases by a constant amount.

 

How to find the sum of the Arithmetic Sequence or Series for the given Series ::

 

When the series contains a large amount of numbers, its impractical to add manually. You can quickly find the sum of any arithmetic sequence by multiplying the average of the first and last term by the number of terms in the sequence.

 

That is given by  S n = n ( a 1 + a n ) 2 Where n = number of terms, a1 = first term, an = last term

 

Here Last term is given by  a n = a 1 + n - 1 d where d = common difference

 

Now given Arithmetic Series is 

 

2, 5, 8, 11,...

 

Here a1 = 2,  d = 3, n = 36 

 

Now,  $$\begin{gathered} a n = a 1 + n - 1 d \\ a 36 = 2 + 36 - 1 3 = 105 + 2 = 107 \end{gathered}$$

 

Now, Sum to 36 terms is given by

 

S 36 = 36 ( 2 + 107 ) 2 = 36 x 109 2 = 3924 2 = 1962

 

 

 

Therefore, Sum to 36 terms of the series 2, 5, 8, 11,... is 1962.

Correct Answer: 45

Explanation:

Here given 

2, 3, 6, 15, ? , 157.5

2 x 1.5 = 3

3 x 2  = 6

6 x 2.5 = 15

15 x 3 = 45

45 x 3.5 = 157.5

Therefore, the missing number is 45

Correct Answer: 98

Explanation:

The given number series is 

3, 5, 8, 15, 28, 51, ?

Here the pattern it follows is

3

3 + 2 = 5 ( add prime number less than 3 i.e, 2)

5 + 3 = 8 (3 is prime number less than 5)

8 + 7 = 15 (7 is prime number less than 8)

15 + 13 = 28 (13 is prime number less than 15)

28 + 23 = 51 (23 is prime number less than 28)

51 + 47 = 98 (47 is prime number less than 51)

 

Hence, the next number in the given number series is 98.

Correct Answer: 635

Explanation:

Given Number series is 18     37     76     155     314     635

 

follows a pattern that, 

 

18

 

18 x 2 +1 = 37

 

37 x 2 +2 = 76

 

76 x 2 +3 = 155

 

155 x 2 +4 = 314

 

314 x 2 +5 = 633 not 635

 

 

 

Hence, the odd man is 635.

Correct Answer: 132

Explanation:

Given series is 

 

12        16         32          68         ?

 

Here it follows a pattern that,

 

12

 

12 + (2x2) = 16

 

16 + (4x4) = 32

 

32 + (6x6) = 68

 

68 + (8x8) = 132

Correct Answer: 28

Explanation:

Here the given series 1, 6,  ?, 15, 45, 66, 91 follows a

Pattern in the series is, +5, +9, +13,...,.. +21, +25

So +4 is getting increased at every term addition.

Missing Number in the series will be 15+(9+4) = 15 + 13 = 28.