## 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 , 8 ,32 , 148 , 765 , 4626 , 32431
1. 765
2. 148
3. 8
4. 32
5. 4626

1. From the given graph , we can see that the increasing order of series as -
First term = 2
Second term = First term + 22 = 8
Third term = Second term + 32 = 32
Similarly , we can calculate all others terms also.

##### Correct Option: D

From the given graph , we can see that the increasing order of series as -
First term = 2
Second term = First term × 2 + 22
Second term = 2 × 2 + 22 = 4 + 4 = 8 ;
Third term = Second term × 3 + 32
Third term = 8 × 3 + 32 = 24 + 9 = 32 ; 32 is wrong. It should be 33.
Similarly , we can find all others terms also.
Fourth term = Third term × 4 + 42
Fourth term = 33 × 4 + 42 = 132 + 16 = 148 ;
Fifth term = Fourth term × 5 + 52
Fifth term = 148 × 5 + 52 = 740 + 25 = 765 ;
Sixth term = Fifth term × 6 + 62
Sixth term = 765 × 6 + 62 = 4590 + 36 = 4626 ;
Seventh term = Sixth term × 7 + 72
Seventh term = 4626 × 7 + 72 = 32382 + 49 = 32431
Hence, 32 is wrong. It should be 33.

1. 108 , 54 , 36 ,18 , 9 , 6 , 4
1. 54
2. 36
3. 18
4. 9
5. 6

1. The given series is in the below pattern,we can see that
Next term = Previous term ÷ n { putting n = 2 and 1.5 alternately }
First term = 108
Second term = First term ÷ 2
Second term = 108 ÷ 2 = 54 ;
Third term = Second term ÷ 1.5
Third term = 54 ÷ 1.5 = 36 ;
Similarly , we can calculate all others terms also.

##### Correct Option: D

The given series is in the below pattern,we can see that
Next term = Previous term ÷ n { putting n = 2 and 1.5 alternately }
First term = 108
Second term = First term ÷ 2
Second term = 108 ÷ 2 = 54 ;
Third term = Second term ÷ 1.5
Third term = 54 ÷ 1.5 = 36 ;
Third term = Third term ÷ 2
Fourth term = 36 ÷ 2 = 18 ;
Fifth term = Fourth term ÷ 1.5
Fifth term = 18 ÷ 1.5 = 9 is wrong. It should be 12.
Sixth term = Fifth term ÷ 2
Sixth term = 12 ÷ 2 = 6 ;
Seventh term = Sixth term ÷ 1.5
Seventh term = 8 ÷ 1.5 = 4
Hence, 9 is wrong. It should be 12.

1. 0 , 1 , 9 , 36 , 99 , 225 , 441
1. 9
2. 36
3. 99
4. 225
5. 441

1. From above given series , we can see that
The differences are given as -
Second term - First term = 1– 0 = 1 = 13;
Third term - Second term = 9 – 1= 8 = 23;
Similarly , we can calculate all others terms also.

##### Correct Option: C

From above given series , we can see that
The differences are given as -
Second term - First term = 1– 0 = 1 = 13;
Third term - Second term = 9 – 1= 8 = 23;
Similarly , we can find all others terms also.
Fourth term - Third term = 36 – 9 = 27 = 33;
Fifth term - Fourth term = 99 – 36 = 63 ≠ 4 3
But , Fifth term - Fourth term = 100 – 36 = 64 = 43;
Here , fifth term 99 is wrong , it should be 100 as fifth term .
Sixth term - Fifth term = 225 – 100 = 125 = 53;
Seventh term - Sixth term = 441– 225 = 216 = 63

1. 2 , 3 , 6 , 15 , 45 , 156.5 , 630
1. 3
2. 45
3. 15
4. 6
5. 156.5

1. As per the details in the question the series is in the form of
First term = 2
Second term = First term × 1.5 = 3
Third term = Second term × 2 = 6
Similarly , we can calculate all next terms also.

##### Correct Option: E

As per the details in the question the series is in the form of
First term = 2
Second term = First term × 1.5
Second term = 2 × 1.5 = 3 ;
Third term = Second term × 2
Third term = 3 × 2 = 6 ;
Similarly , we can find all others terms also.
Fourth term = Third term × 2.5 = 6 × 2.5 = 15 ;
Fifth term = Fourth term × 3 = 15 × 3 = 45 ;
Sixth term = Fifth term × 3.5 = 45 × 3.5 =156.5; 156.5 is wrong. It should be 157.5 .
Seventh term = Sixth term × 4 =157.5 × 4 = 630
Hence, 156.5 is wrong. It should be 157.5.

1. 5 , 8 ,16 , 26 , 50 , 98 ,194
1. 8
2. 26
3. 50
4. 16
5. 98

1. The given series is in the below pattern,
Next term = ( Previous term × 2 ) - 2
First term = 5
Second term = ( First term × 2 ) - 2 = 8 ;
Third term = ( Second term × 2 ) - 2 = 16 ;
Similarly , we can calculate all others terms also.

##### Correct Option: D

The given series is in the below pattern,
Next term = ( Previous term × 2 ) - 2
First term = 5
Second term = ( First term × 2 ) - 2
Second term = ( 5 × 2 ) - 2 = 8 ;
Third term = ( Second term × 2 ) - 2
Third term = ( 8 × 2 ) - 2 = 16; 16 is wrong. It should be 14.
Similarly , we can calculate all others terms also.
Fourth term = ( Third term × 2 ) - 2
Fourth term = ( 14 × 2 ) - 2 = 26 ;
Fifth term = ( Fourth term × 2 ) - 2
Fifth term = ( 26 × 2 ) - 2 = 50 ;
Sixth term = ( Third term × 2 ) - 2
Sixth term = ( 50 × 2 ) - 2 = 98 ;
Seventh term = ( Sixth term × 2 ) - 2
Seventh term = ( 98 × 2 ) - 2 = 194
Hence, 16 is wrong. It should be 14.