Directions (61-65) : Find the wrong number in following number series.

5 , 7 , 17 , 47 , 115 , 235, 467

The correct answer is 235 (which corresponds to Option 235).

To find the wrong number in the given number series, let us analyze the pattern of differences between consecutive terms:

Given series: 5, 7, 17, 47, 115, 235, 467

Let us calculate the differences between consecutive terms:

7 - 5 = 2

17 - 7 = 10

47 - 17 = 30

115 - 47 = 68

Now let us examine the pattern in these differences (2, 10, 30, 68):

$1^3+1=2$

$2^3+2=10$

$3^3+3=30$

$4^3+4=68$

Following this pattern, the next differences should be:

5^th difference = $5^3+5=125+5=130$

6^th difference = $6^3+6=216+6=222$

Now, let us calculate the terms using these correct differences:

First term = 5

Second term = 5 + 2 = 7

Third term = 7 + 10 = 17

Fourth term = 17 + 30 = 47

Fifth term = 47 + 68 = 115

Sixth term = 115 + 130 = 245 (given as 235)

Seventh term = 245 + 222 = 467

Therefore, the term 235 is incorrect and should be replaced by 245.