## 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.  3 10 32 111 460 2315 2 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (b) ?
1. 29
2. 30
3. 26
4. 28
5. None of these

1. The given series is in the below pattern ,
First series :-
First term = 3
Second term = First term × 1 + 7 × 1 = 10
Third term = Second term × 2 + 6 × 2 = 32
similarly , we can calculate the all next terms .
Second series :-
First term = 2
Second term = First term × 1 + 7 × 1 = 9
Third term = Second term × 2 + 6 × 2 = 30

##### Correct Option: B

The given series is in the below pattern ,
First series :-
First term = 3
Second term = First term × 1 + 7 × 1
Second term = 3 × 1 + 7 × 1 = 3 + 7 = 10
Third term = Second term × 2 + 6 × 2
Third term = 10 × 2 + 6 × 2 = 20 + 12 = 32
similarly , we can calculate the all next terms .
Second series :-
First term = 2
Second term = First term × 1 + 7 × 1
Second term = 2 × 1 + 7 × 1 = 2 + 7 = 9
Third term = Second term × 2 + 6 × 2
Third term = 9 × 2 + 6 × 2 = 18 + 12 = 30
Hence , the place value of ( b ) is 30 .

1.  2 3 10 39 172 885 5 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (d) ?
1. 244
2. 175
3. 208
4. 196
5. None of these

1. As per the details in the question the series is in the form of
First series :-
First term = 2
Second term = First term × 1 + 12 = 2 + 1 = 3
Third term = Second term × 2 + 22 = 6 + 4 = 10
similarly , we can calculate the all next terms .
Second series :-
First term = 5
Second term = First term × 1 + 12 = 5 + 1 = 6
Third term = Second term × 2 + 22 = 12 + 4 = 16

##### Correct Option: A

As per the details in the question the series is in the form of
First series :-
First term = 2
Second term = First term × 1 + 12
Second term = 2 × 1 + 1 = 2 + 1 = 3
Third term = Second term × 2 + 22
Third term = 3 × 2 + 4 = 6 + 4 = 10
similarly , we can find the all others terms .
Second series :-
First term = 5
Second term = First term × 1 + 12
Second term = 5 × 1 + 1 = 5 + 1 = 6
Third term = Second term × 2 + 22
Third term = 6 × 2 + 4 = 12 + 4 = 16
Fourth term = Third term × 3 + 32
Fourth term = 16 × 3 + 9 = 57
Fifth term = Fourth term × 4 + 42
Fifth term = 49 × 4 + 16 = 244
Hence , the place value of ( d ) is 244 .

1.  10 11 15 24 40 6 (a) (b) (c) (d) (e) What will come in place of (c) ?
1. 14
2. 13
3. 12
4. 10
5. None of these

1. As per the details in the question the series is in the form of
First series :-
First term = 10
Second term = First term + 12 = 10 + 1 = 11
Third term = Second term + 22 = 11 + 4 = 15
similarly , we can calculate the all next terms .
Second series :-
First term = 6
Second term = First term + 12 = 6 + 1 = 7
Third term = Second term + 22 = 7 + 4 = 11

##### Correct Option: E

As per the details in the question the series is in the form of
First series :-
First term = 10
Second term = First term + 12
Second term = 10 + 12 = 10 + 1 = 11
Third term = Second term + 22
Third term = 11 + 22 = 11 + 4 = 15
similarly , we can find the all others terms .
Second series :-
First term = 6
Second term = First term + 12
Second term = 6 + 12 = 6 + 1 = 7
Third term = Second term + 22
Third term = 7 + 22 = 7 + 4 = 11
Fourth term = Third term + 32
Fourth term = 11 + 32 = 11 + 9 = 20
Hence , the place value of ( c ) is 20 .

1.  12 26 11 36 9 7 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c) ?
1. 7
2. 21
3. 4
4. 11
5. None of these

1. The given series is in the below pattern ,
First series :-
First term = 12
Second term = First term × 2 + 2 = 26
Third term = Second term ÷ 2 - 2 = 11
similarly , we can calculate the all next terms .
........... and so on.
Second series :-
First term = 7
Second term = First term × 2 + 2 = 16
Third term = Second term ÷ 2 - 2 = 6

##### Correct Option: B

The given series is in the below pattern ,
First series :-
First term = 12
Second term = First term × 2 + 2
Second term = 12 × 2 + 2 = 26
Third term = Second term ÷ 2 - 2
Third term = 26 ÷ 2 - 2 = 11
similarly , we can find the all others terms .
........... and so on.
Second series :-
First term = 7
Second term = First term × 2 + 2
Second term = 7 × 2 + 2 = 16
Third term = Second term ÷ 2 - 2
Third term = 16 ÷ 2 - 2 = 6
Fourth term = Third term × 3 + 3
Fourth term = 6 × 3 + 3 = 21
Hence , the place value of ( c ) is 21.

1.  4 5 22 201 12 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (d) ?
1. 4948
2. 4840
3. 4048
4. 4984
5. None of these

1. The given series is in the below pattern ,
First series :-
First term = 4
Second term = First term × 12 + 1 = 4 + 1 = 5
Third term = Second term × 22 + 2 = 20 + 2 = 22
similarly , we can calculate the all next terms .
Second series :-
First term = 12
Second term = First term × 12 + 1 = 12 + 1 = 13
Third term = Second term × 22 + 2 = 52 + 2 = 54

##### Correct Option: E

The given series is in the below pattern ,
First series :-
First term = 4
Second term = First term × 12 + 1
Second term = 4 × 12 + 1 = 4 + 1 = 5
Third term = Second term × 22 + 2
Third term = 5 × 22 + 2 = 20 + 2 = 22
similarly , we can calculate the all next terms .
Second series :-
First term = 12
Second term = First term × 12 + 1
Second term = 12 × 12 + 1 = 12 + 1 = 13
Third term = Second term × 22 + 2
Third term = 13 × 22 + 2 = 52 + 2 = 54
Fourth term = Third term × 32 + 3
Fourth term = 54 × 32 + 3 = 486 + 3 = 489
Fifth term = Fourth term × 42 + 4
Fifth term = 489 × 42 + 4 = 7824 + 4 = 7828
Hence , the place value of ( d ) is 7828 .