## 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.  2 3 7 25 121 721 3 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c) ?

1. The given series is in the below pattern ,
First series :-
First term = 2
Second term = First term × 2 - 1 = 3
Third term = Second term × 3 - 2 = 7
similarly , we can calculate the all next terms .
Second series :-
First term = 3
Second term = First term × 2 - 1 = 5
Third term = Second term × 3 - 2 = 13

##### Correct Option: B

The series is × 2 –1, × 3 – 2, × 4 – 3,.....
The given series is in the below pattern ,
First series :-
First term = 2
Second term = First term × 2 - 1
Second term = 2 × 2 - 1 = 3
Third term = Second term × 3 - 2
Third term = 3 × 3 - 2 = 7
similarly , we can calculate the all next terms .
Second series :-
First term = 3
Second term = First term × 2 - 1
Second term = 3 × 2 - 1 = 5
Third term = Second term × 3 - 2
Third term = 5 × 3 - 2 = 13
Fourth term = Third term × 4 - 3
Fourth term = 13 × 4 - 3 = 49
Hence , the place value of ( c ) is 49 .

1.  1 8 10 35 136 2 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c) ?

1. As per the details in the question the series is in the form of
First series :-
First term = 1
Second term = First term × 1 + 7 = 8
Third term = Second term × 2 - 6 = 10
similarly , we can calculate the all next terms .
Second series :-
First term = 2
Second term = First term × 1 + 7 = 9
Third term = Second term × 2 - 6 = 12

##### Correct Option: E

As per the details in the question the series is in the form of
First series :-
First term = 1
Second term = First term × 1 + 7
Second term = 1 × 1 + 7 = 8
Third term = Second term × 2 - 6
Third term = 8 × 2 - 6 = 10
similarly , we can find the all others terms .
Second series :-
First term = 2
Second term = First term × 1 + 7
Second term = 2 × 1 + 7 = 9
Third term = Second term × 2 - 6
Third term = 9 × 2 - 6 = 12
Fourth term = Third term × 3 + 5
Fourth term = 12 × 3 + 5 = 41
Hence , the place value of ( c ) is 41 .

1.  9 19.5 41 84.5 12 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c) ?

1. As per the details in the question the series is in the form of
First series :-
First term = 9
Second term = First term × 2 + 1.5 = 19.5
Third term = Second term × 2 + 2 = 41
similarly , we can calculate the all next terms .
Second series :-
First term = 12
Second term = First term × 2 + 1.5 = 25.5
Third term = Second term × 2 + 2 = 53

##### Correct Option: E

As per the details in the question the series is in the form of
First series :-
First term = 9
Second term = First term × 2 + 1.5 = 19.5
Third term = Second term × 2 + 2 = 41
similarly , we can calculate the all next terms .
Second series :-
First term = 12
Second term = First term × 2 + 1.5 = 25.5
Third term = Second term × 2 + 2 = 53
Fourth term = Third term × 2 + 2.5
Fourth term = 53 × 2 + 2.5 = 108.5
So, 108.5 should come in place of (c).

1.  38 19 28.5 71.25 18 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (d) ?

1. The given series is in the below pattern ,
First series :-
First term = 38
Second term = First term × 0.5 = 19
Third term = Second term × 1.5 = 28.5
similarly , we can calculate the all next terms .
Second series :-
First term = 18
Second term = First term × 0.5 = 9
Third term = Second term × 1.5 = 13.5

##### Correct Option: D

The given series is in the below pattern ,
First series :-
First term = 38
Second term = First term × 0.5
Second term = 38 × 0.5 = 19
Third term = Second term × 1.5
Third term = 19 × 1.5 = 28.5
similarly , we can find the all others terms .
Second series :-
First term = 18
Second term = First term × 0.5
Second term = 18 × 0.5 = 9
Third term = Second term × 1.5
Third term = 9 × 1.5 = 13.5
Fourth term = Third term × 2.5
Fourth term = 13.5 × 2.5 = 33.75
Fifth term = Fourth term × 3.5
Fifth term = 33.75 × 3.5 = 118.125
So 118.125 should come in place of (d).

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, 13, 65, 271, 817, 1639, 1645

1. The given series is in the below pattern,
First term = 2
Second term = ( First term × 6 ) + 1 = 13
Similarly we can find the all terms

##### Correct Option: B

The given series is in the below pattern,
First term = 2
Second term = ( First term × 6 ) + 1 = 13
Third term = ( Second term × 5 ) + 2 = 65 , 67 should be sixth term because ( 13 × 5 ) + 2 = 67 .
So 65 is wrong. we get 67 as Third term.
Similarly we can find the all terms
Fourth term = ( Third term × 4 ) + 3 = 271
Fifth term = ( Fourth term × 3 ) + 2 = 817
Sixth term = 1639,
Seventh term = 1645.