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.

25 146 65 114 39 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (e) ?

 122
 119
 112
 94
 None of these

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The given series is in the below pattern ,
First series :
First term = 25
Second term = First term + 11^{2} = 25 + 121 = 146
Third term = Second term  9^{2} = 146  81 = 65
similarly , we can calculate the all next terms .
Second series :
First term = 39
Second term = First term + 11^{2} = 39 + 121 = 160
Third term = Second term  9^{2} = 160  81 = 79Correct Option: C
The given series is in the below pattern ,
First series :
First term = 25
Second term = First term + 11^{2}
⇒ Second term = 25 + 11^{2} = 25 + 121 = 146
Third term = Second term  9^{2}
⇒ Third term = 146  9^{2} = 146  81 = 65
similarly , we can calculate the all next terms .
Second series :
First term = 39
Second term = First term + 11^{2}
⇒ Second term = 39 + 11^{2} = 39 + 121 = 160
Third term = Second term  9^{2}
⇒ Third term = 160  9^{2} = 160  81 = 79
Fourth term = Third term + 7^{2}
⇒ Fourth term = 79 + 7^{2} = 79 + 49 = 128
Fifth term = Fourth term  5^{2}
⇒ Fifth term = 128  5^{2} = 128  25 = 103
Fifth term = Fourth term  5^{2}
⇒ Sixth term = 103 + 3^{2} = 103 + 9 = 112
So 112 should come in place of (e).
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, 4.5, 11, 30, 92.5, 329

 92.5
 4.5
 11
 2
 30

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As per the details in the question the series is in the form of
First term = 1
Second term = ( First term × Variable ) + Variable = 2
Third term = ( Second term × Variable + 0.5 ) + Variable + 0.5 = 4.5Correct Option: A
As per the details in the question the series is in the form of
First term = 1
Second term = ( First term × Variable ) + Variable = 2
Third term = ( Second term × Previous Variable + 0.5 ) + Previous Variable + 0.5 = 4.5
Similarly we can find the all others terms
Second term = ( 1 × 1 ) + 1 = 2
Third term = ( 2 × 1.5 ) + 1.5 = 4.5
Fourth term = ( 4.5 × 2 ) + 2 = 11
Fifth term = (11 × 2.5 ) + 2.5 = 30
Sixth term = ( 30 × 3 ) + 3 = 92.5 , 93 should be sixth term because ( 30 × 3 ) + 3 = 93
So 92.5 is wrong. we get 93 as 6th term.
Seventh term = ( 93 × 3.5 ) + 3.5 = 325.5 + 3.5 = 329.
 2, 5, 7, 12, 19, 32, 50

 7
 12
 32
 19
 5

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The Order of above given series is
First term + Second term = Third term
⇒ 2 + 5 = 7;
Second term + Third term = Fourth term
⇒ 5 + 7 = 12;
Third term + Fourth term = Fifth term
⇒ 7 + 12 = 19;...
Correct Option: C
The Order of above given series is
First term + Second term = Third term
⇒ 2 + 5 = 7;
Second term + Third term = Fourth term
⇒ 5 + 7 = 12;
Third term + Fourth term = Fifth term
⇒ 7 + 12 = 19;...
Fourth term + Fifth term = Sixth term
⇒ 12 + 19 = 32 , 31 should be 6th term because 12 + 19 = 31
So 32 is wrong. we get 31 as 6th term.
Fifth term + Sixth term = Seventh term
⇒ 19 + 31 = 50
 2, 14, 91, 546, 3002, 15015

 15015
 91
 14
 3002
 546

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The given series is in the below pattern,
∴ First term = 2
Second term = First term × 7
Similarly we can calculate next terms also.Correct Option: D
The given series is in the below pattern,
∴ First term = 2
Second term = First term × 7
⇒ Second term = 2 × 7 = 14
Similarly we can find the all others terms also.
Third term = Second term × 6.5
⇒ Third term = 14 × 6.5 = 91
Fourth term = Third term × 6
⇒ Fourth term = 91 × 6 = 546
Fifth term = Fourth term × 5.5
⇒ Fifth term = 546 × 5.5 = 3002 is wrong , So 3003 should be Fifth term because ( 546 × 5.5 ) = 3003 .
Sixth term = Fifth term × 5
⇒ Fifth term = 3003 × 5 = 15015.
Direction: What will come in the place of question mark (?) in the following number.
 0, 7, 26, 63, ?

 125
 126
 217
 124
 None of these

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The given series is in the below pattern,we can see that
Next term ( T_{n} ) = n^{3}  1 { where , putting n = 1 , 2 , 3 , 4 , 5 respectively }Correct Option: D
The given series is in the below pattern,we can see that
Next term ( T_{n} ) = n^{3}  1 { where , putting n = 1 , 2 , 3 , 4 , 5 respectively }
First term = T_{1} = 1^{3}  1 = 0
Second term = T_{2} = 2^{3}  1 = 7
Similarly we can find the all others terms
Third term = 26
Fourth term = 63
Fifth term( ? )= 124
Hence we get the value of ? = 124