## Number Series

#### Number Series

Direction: In each of these questions a number series is given. Only one number is wrong in each series. You have to find out the wrong number.

1. 2 , 3 , 11 , 38 ,102 , 229 , 443

1. The given series is in the below pattern,
First term = 2
Second term = First term + 13 = 3
Third term = Second term + 23 = 11
Similarly , we can calculate all others terms also.

##### Correct Option: B

The given series is in the below pattern,
First term = 2
Second term = First term + 13
Second term = 2 + 13 = 3 ;
Third term = Second term + 23
Third term = 3 + 23 = 11 ;
Similarly , we can find the all others terms also.
Fourth term = Third term + 42
Fourth term = 11 + 33 = 38 ;
Fifth term = Fourth term + 52
Fifth term = 38 + 43 = 102
Sixth term = Fifth term + 62
Sixth term = 102 + 53 = 229 ; 229 is wrong. It should be 227.
Seventh term = Sixth term + 72
Seventh term = 227 + 63 = 443
Hence, 229 is wrong. It should be 227.

1. 2807, 1400, 697, 347, 171, 84, 41, 20

1. From the given figure , we can see that
First term = 2807
Second term = ( First term - 7 ) ÷ 2 = 1400
Third term = ( Second term - 6 ) ÷ 2 = 697

##### Correct Option: B

From the given figure , we can see that
First term = 2807
Second term = ( First term - 7 ) ÷ 2 = 1400
Third term = ( Second term - 6 ) ÷ 2 = 697
Second term = ( 2807 - 7 ) ÷ 2 = 1400 ;
Third term = ( 1400 - 6 ) ÷ 2 = 697 ;
Fourth term = ( 697 - 5 ) ÷ 2 = 347; 347 is wrong. It should be 346.
Fifth term = ( 346 - 4 ) ÷ 2 = 171 ;
Sixth term = ( 171 - 3 ) ÷ 2 = 84 ;
Seventh term = ( 84 - 2 ) ÷ 2 = 41 ;
Eighth term = ( 41 - 1 ) ÷ 2 = 20
Hence, 347 is wrong. It should be 346.

1. 2 , 3 , 5 , 8 , 14 , 23 , 41, 69

1. The series is an alternate series, having
Next term = ( Previous term × 3 ) - 1
Odd position series :-
First term = 2
Third term = ( First term × 3 ) - 1
.........................and so on .
Even position series :-
Second term = 3
Fourth term = ( Second term × 3 ) - 1
.........................and so on .

##### Correct Option: E

The series is an alternate series, having
Odd position series :-
First term = 2
Third term = ( First term × 3 ) - 1
Third term = ( 2 × 3 ) - 1 = 5 ;
Fifth term = ( Third term × 3 ) - 1
Fifth term = ( 5 × 3 ) - 1 = 14 ;
Seventh term = ( Fifth term × 3 ) - 1
Seventh term = ( 14 × 3 ) - 1 = 41 ;
Even position series :-
Second term = 3
Fourth term = ( Second term × 3 ) - 1
Fourth term = ( 3 × 3 ) - 1 = 8 ;
Sixth term = ( Fourth term × 3 ) - 1
Sixth term = ( 8 × 3 ) - 1 = 23 ;
Eighth term = ( Sixth term × 3 ) - 1
Eighth term = ( 23 × 3 ) - 1 = 69; 69 is wrong. It should be 68.

1. 3 , 7. 5 ,15 , 37.5 , 75 ,167.5 , 375

1. The given series is in the below pattern,
First term = 3
Second term = First term × 2.5 = 7.5 ;
Third term = Second term × 2 = 15 ;
Similarly , we can calculate all others terms also.

##### Correct Option: A

The given series is in the below pattern,
First term = 3
Second term = First term × 2.5
Second term = 3 × 2.5 = 7.5 ;
Third term = Second term × 2
Third term = 7.5 × 2 = 15 ;
Fourth term = Third term × 2.5
Fourth term = 15 × 2.5 = 37.5 ;
Fifth term = Fourth term × 2
Fifth term = 37.5 × 2 = 75 ;
Sixth term = Fifth term × 2.5
Sixth term = 75 × 2.5 = 167.5; 167.5 is wrong. It should be 187.5.
Seventh term = Sixth term × 2
Seventh term = 187.5 × 2 = 375 ;
Hence, 167.5 is wrong. It should be 187.5.

1. 36 , 20 , 12 , 8 , 6 , 5.5 , 4.5

1. The given series is in the below pattern,we can see that
Difference between all terms are given as :- 16 ÷ 2 = 8 , 8 ÷ 2 = 4 , 4 ÷ 2 = 2 , 2 ÷ 2 = 1 , 1 ÷ 2 = 0.5 .
First term = 36
Second term = First term - 16 = 20 ;
Third term = Second term - 8 = 12 ;
Similarly , we can calculate all next terms also.

##### Correct Option: A

As per given above series , it is clear that
Difference between all terms are given as :- 16 ÷ 2 = 8 , 8 ÷ 2 = 4 , 4 ÷ 2 = 2 , 2 ÷ 2 = 1 , 1 ÷ 2 = 0.5 .
First term = 36
Second term = First term - 16
Second term = 36 - 16 = 20 ;
Third term = Second term - 8
Third term = 20 - 8 = 12 ;
Similarly , we can find all others terms also.
Fourth term = Third term - 4 = 12 - 4 = 8 ;
Fifth term = Fourth term - 2 = 8 - 2 = 6 ;
Sixth term = Fifth term - 1 = 6 - 1 = 5.5; 5.5 is wrong. It should be 5 .
Seventh term = Sixth term - 0.5 = 5 - 0.5 = 4.5
Hence, 5.5 is wrong. It should be 5 as Sixth term .