Number Series
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.
 2 , 3 , 11 , 38 ,102 , 229 , 443

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The given series is in the below pattern,
First term = 2
Second term = First term + 1^{3} = 3
Third term = Second term + 2^{3} = 11
Similarly , we can calculate all others terms also.Correct Option: B
The given series is in the below pattern,
First term = 2
Second term = First term + 1^{3}
⇒ Second term = 2 + 1^{3} = 3 ;
Third term = Second term + 2^{3}
⇒ Third term = 3 + 2^{3} = 11 ;
Similarly , we can find the all others terms also.
Fourth term = Third term + 4^{2}
⇒ Fourth term = 11 + 3^{3} = 38 ;
Fifth term = Fourth term + 5^{2}
⇒ Fifth term = 38 + 4^{3} = 102
Sixth term = Fifth term + 6^{2}
⇒ Sixth term = 102 + 5^{3} = 229 ; 229 is wrong. It should be 227.
Seventh term = Sixth term + 7^{2}
⇒ Seventh term = 227 + 6^{3} = 443
Hence, 229 is wrong. It should be 227.
 2807, 1400, 697, 347, 171, 84, 41, 20

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From the given figure , we can see that
First term = 2807
Second term = ( First term  7 ) ÷ 2 = 1400
Third term = ( Second term  6 ) ÷ 2 = 697Correct Option: B
From the given figure , we can see that
First term = 2807
Second term = ( First term  7 ) ÷ 2 = 1400
Third term = ( Second term  6 ) ÷ 2 = 697
⇒ Second term = ( 2807  7 ) ÷ 2 = 1400 ;
⇒ Third term = ( 1400  6 ) ÷ 2 = 697 ;
⇒ Fourth term = ( 697  5 ) ÷ 2 = 347; 347 is wrong. It should be 346.
⇒ Fifth term = ( 346  4 ) ÷ 2 = 171 ;
⇒ Sixth term = ( 171  3 ) ÷ 2 = 84 ;
⇒ Seventh term = ( 84  2 ) ÷ 2 = 41 ;
⇒ Eighth term = ( 41  1 ) ÷ 2 = 20
Hence, 347 is wrong. It should be 346.
 2 , 3 , 5 , 8 , 14 , 23 , 41, 69

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The series is an alternate series, having
Next term = ( Previous term × 3 )  1
Odd position series :
First term = 2
Third term = ( First term × 3 )  1
.........................and so on .
Even position series :
Second term = 3
Fourth term = ( Second term × 3 )  1
.........................and so on .Correct Option: E
The series is an alternate series, having
Odd position series :
First term = 2
Third term = ( First term × 3 )  1
⇒ Third term = ( 2 × 3 )  1 = 5 ;
Fifth term = ( Third term × 3 )  1
⇒ Fifth term = ( 5 × 3 )  1 = 14 ;
Seventh term = ( Fifth term × 3 )  1
⇒Seventh term = ( 14 × 3 )  1 = 41 ;
Even position series :
Second term = 3
Fourth term = ( Second term × 3 )  1
⇒ Fourth term = ( 3 × 3 )  1 = 8 ;
Sixth term = ( Fourth term × 3 )  1
⇒ Sixth term = ( 8 × 3 )  1 = 23 ;
Eighth term = ( Sixth term × 3 )  1
⇒ Eighth term = ( 23 × 3 )  1 = 69; 69 is wrong. It should be 68.
 3 , 7. 5 ,15 , 37.5 , 75 ,167.5 , 375

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The given series is in the below pattern,
First term = 3
Second term = First term × 2.5 = 7.5 ;
Third term = Second term × 2 = 15 ;
Similarly , we can calculate all others terms also.Correct Option: A
The given series is in the below pattern,
First term = 3
Second term = First term × 2.5
⇒ Second term = 3 × 2.5 = 7.5 ;
Third term = Second term × 2
⇒ Third term = 7.5 × 2 = 15 ;
Fourth term = Third term × 2.5
⇒ Fourth term = 15 × 2.5 = 37.5 ;
Fifth term = Fourth term × 2
⇒ Fifth term = 37.5 × 2 = 75 ;
Sixth term = Fifth term × 2.5
⇒ Sixth term = 75 × 2.5 = 167.5; 167.5 is wrong. It should be 187.5.
Seventh term = Sixth term × 2
⇒ Seventh term = 187.5 × 2 = 375 ;
Hence, 167.5 is wrong. It should be 187.5.
 36 , 20 , 12 , 8 , 6 , 5.5 , 4.5

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The given series is in the below pattern,we can see that
Difference between all terms are given as : 16 ÷ 2 = 8 , 8 ÷ 2 = 4 , 4 ÷ 2 = 2 , 2 ÷ 2 = 1 , 1 ÷ 2 = 0.5 .
First term = 36
Second term = First term  16 = 20 ;
Third term = Second term  8 = 12 ;
Similarly , we can calculate all next terms also.Correct Option: A
As per given above series , it is clear that
Difference between all terms are given as : 16 ÷ 2 = 8 , 8 ÷ 2 = 4 , 4 ÷ 2 = 2 , 2 ÷ 2 = 1 , 1 ÷ 2 = 0.5 .
First term = 36
Second term = First term  16
⇒ Second term = 36  16 = 20 ;
Third term = Second term  8
⇒ Third term = 20  8 = 12 ;
Similarly , we can find all others terms also.
Fourth term = Third term  4 = 12  4 = 8 ;
Fifth term = Fourth term  2 = 8  2 = 6 ;
Sixth term = Fifth term  1 = 6  1 = 5.5; 5.5 is wrong. It should be 5 .
Seventh term = Sixth term  0.5 = 5  0.5 = 4.5
Hence, 5.5 is wrong. It should be 5 as Sixth term .