In the given number series which follows the definite rules then find out the value of (M, N, O, and P) in second number series. 7 18 42 94 204 4 M N O P What value will come in place of P?

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: 32

Explanation:

Here the given series follows a pattern that,

2² - 0 = 4  

3² - 1 = 8  

4² - 2 = 14

5² - 3 = 22

6² - 4 = 32

Hence, the missing number is 32

 

 

Method 2 ::

The difference between 4 and 8 is 4, the difference between 8 and 14 is 6, the difference between 14 and 22 is 8. So the next difference between 22 and the next number will be 10 since it follows (4,6,8,10 - add +2 each time)

Hence, 22 + 10 = 32 is the missing number.

Correct Answer: 245

Explanation:

Given 311   230   294   ?   281   256

 

311 - (9x9) = 230

 

230 + (8x8) = 294

 

294 - (7x7) = 245

 

245 + (6x6) = 281

 

281 - (5x5) = 256

 

Hence, the missing number in the given series is 245.

Correct Answer: 54055

Explanation:

Here the given series follows a pattern that, multiplying the number with odd numbers in decreasing order starting with 13. That is,

 

6 × 13 = 78

 

65 × 11 = 858

 

858 × 9 = 7722

 

7722 × 7 = 54054

 

54054 × 5 = 270270

 

Hence, the wrong number is 54055

Correct Answer: Horse

Explanation:

Except Horse, remaining all belong to female category.

Hind - Female Deer

Ewe - Female Sheep

Bitch - Female Dog. 

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: 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: 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: 980

Explanation:

The given series follows the pattern that,

 

×5+5,   ×5+5,   ×5+5,   ×5+5,   ×5+5

 

38 x 5 + 5  = 195

 

195 x 5 + 5 = 980

 

980 x 5 + 5 = 4905

 

4905 x 5 + 5 = 24530

 

24530 x 5 + 5 = 122655

 

So the missing number is 980 .

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