Odd Man Out Questions

Here the given number series is 270, 261, 279, 252, 289, 243

270 - 9 = 261

261 + 18 = 279

279 - 27 = 252

252 + 36 = 288 (not equals to 289)

288 - 45 = 243

Hence, the odd number in the given number series is 289.

The given number series is 3, 11, 80, 291, 803

$$\begin{gathered} 3 \\ 3 + 23 = 3 + 8 = 11 \\ 11 + 43 = 11 + 64 = 75 (not 80) \\ 75 + 63 = 75 + 216 = 291 \\ 291 + 83 = 291 + 512 = 803 \end{gathered}$$

The given number series 8, 18, 56, 232, 1165 

8

8 x 2 + 2 = 18

18 x 3 + 3 = 57 (not 56)

57 x 4 + 4 = 232

232 x 5 + 5 = 1165

Hence, the odd man in the given series is 56.

The given number series 2, 19, 0, 21, –2, ? follows a pattern,

2

2 + 17 = 19

19 - 19 = 0

0 + 21 = 21

21 - 23 = -2

-2 + 25 = 23

Hence, the next number in the series is 23.

The given number series is 3  24  186  1008  5040  20160

Here  the given series follows a pattern that,

3

3 x 8 = 24

24 x 7 = 168 not 186

168 x 6 = 1008

1008 x 5 =  5040

5040 x 4 = 20160

Hence the Odd One in the number series is 186.

Given number sequence is 28, 16, 28, 76, 274

Here the sequence follows a pattern that

28

28 x 0.5 + 2 = 14 + 2 = 16

16 x 1.5 + 4 = 24 + 4 = 28

28 x 2.5 + 6 = 70 + 6 = 76

76 x 3.5 + 8 = 266 + 8 = 274

274 x 4.5 + 10 = 1233 + 10 = 1243

Hence, the next number in the given number sequence is 1243.

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 Sn = n(a1 + an)2 Where n = number of terms, a1 = first term, an = last term

Here Last term is given by an = a1 + n-1d where d = common difference

Now given Arithmetic Series is 

2, 5, 8, 11,...

Here a1 = 2,  d = 3, n = 36 

Now, $$\begin{gathered} an= a1 + n - 1d \\ a36= 2 + 36 - 13 = 105 + 2 = 107 \end{gathered}$$

Now, Sum to 36 terms is given by

S36 = 36(2 + 107)2 = 36 x 1092 = 39242 = 1962

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

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