## Number Series

#### Number Series

Direction: In each of the following questions a number series is given. A number is given after the series and then (a), (b), (c), (d) and (e) are given. According to the given series, you have to form a new series which begins with the given number, and then answer the question asked.

1.  6 3.0 4.5 2.25 4.0 12 40 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c) ?
1. 20.5
2. 21.5
3. 33.75
4. 69.5
5. 15

1. The given series is in the below pattern ,
First series :-
First term = 6
Second term = First term ÷ 2 = 3
Third term = Second term × 1.5 = 4.5
similarly , we can calculate the all next terms .
........... and so on.
Second series :-
First term = 40
Second term = First term ÷ 2 = 20
Third term = Second term × 1.5 = 30

##### Correct Option: E

The given series is in the below pattern ,
First series :-
First term = 6
Second term = First term ÷ 2
Second term = 6 ÷ 2 = 3
Third term = Second term × 1.5
Third term = 3 × 1.5 = 4.5
similarly , we can calculate the all next terms .
........... and so on.
Second series :-
First term = 40
Second term = First term ÷ 2
Second term = 40 ÷ 2 = 20
Third term = Second term × 1.5
Third term = 20 × 1.5 = 30
Fourth term = Third term ÷ 2
Fourth term = 30 ÷ 2 = 15
Hence , the place value of (c) is 15 .

1.  4 9 25 103 3 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c) ?
1. 391
2. 81
3. 91
4. 79
5. None of these

1. The given series is in the below pattern ,
First series :-
First term = 4
Second term = First term × 2 + 1 = 9
Third term = Second term × 3 - 2 = 25
similarly , we can calculate the all next terms .
Second series :-
First term = 3
Second term = First term × 2 + 1 = 7
Third term = Second term × 3 - 2 = 19

##### Correct Option: D

The given series is in the below pattern ,
First series :-
First term = 4
Second term = First term × 2 + 1
Second term = 4 × 2 + 1 = 9
Third term = Second term × 3 - 2
Third term = 9 × 3 - 2 = 25
similarly , we can find the all others terms .
......... and so on .
Second series :-
First term = 3
Second term = First term × 2 + 1
Second term = 3 × 2 + 1 = 7
Third term = Second term × 3 - 2
Third term = 7 × 3 - 2 = 19
Fourth term = Third term × 4 + 3
Fourth term = 19 × 4 + 3 = 79
Hence , the place value of ( c ) is 79 .

1.  6 10 32 126 2 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (a) ?
1. 4
2. 6
3. 2
4. 3
5. None of these

1. The series is × 2 – 2, × 3 + 2, × 4 – 2,...
The given series is in the below pattern ,
First series :-
First term = 6
Second term = First term × 2 - 2 = 10
Third term = Second term × 3 + 2 = 32
similarly , we can calculate the all next terms .
Second series :-
First term = 2
Second term = First term × 2 - 2
Third term = Second term × 3 + 2

##### Correct Option: C

The given series is in the below pattern ,
First series :-
First term = 6
Second term = First term × 2 - 2
Second term = 6 × 2 - 2 = 10
Third term = Second term × 3 + 2
Third term = 10 × 3 + 2 = 32
similarly , we can find the all others terms .
......... and so on .
Second series :-
First term = 2
Second term = First term × 2 - 2
Second term = 2 × 2 - 2 = 2
Hence , the place value of ( a ) is 2 .

1.  7 4 5 9 20 52.5 3 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c) ?
1. 4.5
2. 2
3. 6
4. 7
5. None of these

1. As per the details in the question the series is in the form of
First series :-
First term = 7
Second term = First term × 0.5 + 0.5 = 4
Third term = Second term × 1 + 1 = 5
similarly , we can calculate the all next terms .
Second series :-
First term = 3
Second term = First term × 0.5 + 0.5 = 2
Third term = Second term × 1 + 1 = 3

##### Correct Option: C

As per the details in the question the series is in the form of
First series :-
First term = 7
Second term = First term × 0.5 + 0.5
Second term = 7 × 0.5 + 0.5 = 4
Third term = Second term × 1 + 1
Third term = 4 × 1 + 1 = 5
similarly , we can find the all others terms .
Second series :-
First term = 3
Second term = First term × 0.5 + 0.5
Second term = 3 × 0.5 + 0.5 = 2
Third term = Second term × 1 + 1
Third term = 2 × 1 + 1 = 3
Fourth term = Third term × 1.5 + 1.5
Fourth term = 3 × 1.5 + 1.5 = 6
Hence , the place value of ( c ) is 6 .

1.  3 12 30 66 138 282 7 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (b) ?
1. 34
2. 70
3. 46
4. 62
5. None of these

1. As per the details in the question the series is in the form of
First series :-
First term = 3
Second term = First term × 2 + 6 = 12
Third term = Second term × 2 + 6 = 30
similarly , we can calculate the all next terms .
Second series :-
First term = 7
Second term = First term × 2 + 6 = 20
Third term = Second term × 2 + 6 = 46

##### Correct Option: C

As per the details in the question the series is in the form of
First series :-
First term = 3
Second term = First term × 2 + 6
Second term = 3 × 2 + 6 = 12
Third term = Second term × 2 + 6
Third term = 12 × 2 + 6 = 30
similarly , we can find the all others terms .
Second series :-
First term = 7
Second term = First term × 2 + 6
Second term = 7 × 2 + 6 = 20
Third term = Second term × 2 + 6
Third term = 20 × 2 + 6 = 46
Hence , the place value of ( b ) is 46 .