## Number Series

#### Number Series

Direction: Directions : What will come in the place of question mark (?) in the following number.

1. 4 , 2 , ?, 7.5, 26.25, 118.125
1. 5
2. 4
3. 3.5
4. 3
5. 4.5

1. As per the details in the question the series is in the form of
First term = 4
Second term = First term × 0.5
Second term = 4 × 0.5 = 2
Third term = Second term × 1.5
Third term = 2 × 1.5 = ?
∴ ? = 3
Similarly , we can calculate all next terms also.

##### Correct Option: D

As per the details in the question the series is in the form of
First term = 4
Second term = First term × 0.5
Second term = 4 × 0.5 = 2
Third term = Second term × 1.5
Third term = 2 × 1.5 = ?
∴ ? = 3
Fourth term = Third term × 2.5
Fourth term = 3 × 2.5 = 7.5 ;
Fifth term = Fourth term × 3.5
Fifth term = 7.5 × 3.5 = 26.25 ;
Similarly , we can find all others terms also.
Sixth term = Fifth term × 4.5
Sixth term = 26.25 × 4.5 = 118.125;
Hence , Third term = 3

1. 16, ?, 21, 30, 46, 71, 107
1. 17
2. 19
3. 21
4. 23
5. 25

1. The given series is in the below pattern,
First term = 16
Second term = First term + 12 = ?
Second term = 16 + 12 = 17
∴ ? = 17
Third term = Second term 12 = 15 ;
Similarly , we can calculate all others terms also.

##### Correct Option: A

The given series is in the below pattern,
First term = 16
Second term = First term + 12
Second term = 16 + 12 = 17
∴ ? = 17
Third term = Second term + 22
Third term = 17 + 22 = 21
Fourth term = Third term + 32
Fourth term = 21 + 32 = 30 ;
Fifth term = Fourth term + 42
Fifth term = 30 + 42 = 46 ;
Similarly , we can find all others terms also.
Sixth term = Fifth term + 52
Sixth term = 46 + 52 = 71;
Seventh term = Sixth term + 62
Sixth term = 71 + 62 = 107
Hence , Second term = 17

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.  5 9 26 90 13 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (e) ?
1. 2880
2. 2292
3. 1716
4. 3432
5. None of these

1. The given series is in the below pattern ,
First series :-
First term = 5
Second term = First term × 1 + 4 = 9
Third term = Second term × 2 + 8 = 26
similarly , we can calculate the all next terms .
Second series :-
First term = 13
Second term = First term × 1 + 4 = 17
Third term = Second term × 2 + 8 = 42

##### Correct Option: E

The given series is in the below pattern ,
First series :-
First term = 5
Second term = First term × 1 + 4
Second term = 5 × 1 + 4 = 9
Third term = Second term × 2 + 8
Third term = 9 × 2 + 8 = 26
similarly , we can find the all others terms .
......... and so on .
Second series :-
First term = 13
Second term = First term × 1 + 4
Second term = 13 × 1 + 4 = 17
Third term = Second term × 2 + 8
Third term = 17 × 2 + 8 = 42
Fourth term = Third term × 3 + 12
Fourth term = 42 × 3 + 12 = 138
Fifth term = Fourth term × 4 + 16
Fifth term = 138 × 4 + 16 = 568
Sixth term = Fifth term × 5 + 20
Sixth term = 568 × 5 + 20 = 2860
Hence , the place value of ( e ) is 2860 .

1.  1260 628 312 154 788 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (d) ?
1. 194
2. 45.5
3. 48
4. 72.5
5. None of these.

1. As per the details of question is given series in the form of ,
First series :-
First term = 1260
Second term = First term ÷ 2 - 2
Second term = 1260 ÷ 2 - 2 = 628
Third term = Second term ÷ 2 - 2
Third term = 628 ÷ 2 - 2 = 312
similarly , we can find the all others terms .
......... and so on .
Second series :-
First term = 788
Second term = First term ÷ 2 - 2 = 392
Third term = Second term ÷ 2 - 2 = 194

##### Correct Option: B

As per the details of question is given series in the form of ,
First series :-
First term = 1260
Second term = First term ÷ 2 - 2
Second term = 1260 ÷ 2 - 2 = 628
Third term = Second term ÷ 2 - 2
Third term = 628 ÷ 2 - 2 = 312
similarly , we can find the all others terms .
......... and so on .
Second series :-
First term = 788
Second term = First term ÷ 2 - 2
Second term = 788 ÷ 2 - 2 = 392
Third term = Second term ÷ 2 - 2
Third term = 392 ÷ 2 - 2 = 194
Fourth term = Third term ÷ 2 - 2
Fourth term = 194 ÷ 2 - 2 = 95
Fifth term = Fourth term ÷ 2 - 2
Fifth term = 95 ÷ 2 - 2 = 45.5
Hence , the place value of ( d ) is 45.5 .

1.  5 6 16 57 244 1245 2 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (d) ?
1. 46
2. 39
3. 156
4. 173
5. None of these

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

##### Correct Option: E

As per the details in the question the series is in the form of
First series :-
First term = 5
Second term = First term × 1 + 12
Second term = 5 × 1 + 1 = 6
Third term = Second term × 2 + 22
Third term = 6 × 2 + 4 = 16
similarly , we can find the all others terms .
Second series :-
First term = 2
Second term = First term × 1 + 12
Second term = 2 × 1 + 1 = 3
Third term = Second term × 2 + 22
Third term = 3 × 2 + 4 = 10
Fourth term = Third term × 3 + 32
Fourth term = 10 × 3 + 9 = 39
Fifth term = Fourth term × 4 + 42
Fifth term = 39 × 4 + 16 = 172
Hence , the place value of ( d ) is 172 .