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.

3 10 32 111 460 2315 2 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (b) ?

 29
 30
 26
 28
 None of these

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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 = 30Correct 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 .

2 3 10 39 172 885 5 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (d) ?

 244
 175
 208
 196
 None of these

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As per the details in the question the series is in the form of
First series :
First term = 2
Second term = First term × 1 + 1^{2} = 2 + 1 = 3
Third term = Second term × 2 + 2^{2} = 6 + 4 = 10
similarly , we can calculate the all next terms .
Second series :
First term = 5
Second term = First term × 1 + 1^{2} = 5 + 1 = 6
Third term = Second term × 2 + 2^{2} = 12 + 4 = 16Correct 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 + 1^{2}
⇒ Second term = 2 × 1 + 1 = 2 + 1 = 3
Third term = Second term × 2 + 2^{2}
⇒ 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 + 1^{2}
⇒ Second term = 5 × 1 + 1 = 5 + 1 = 6
Third term = Second term × 2 + 2^{2}
⇒ Third term = 6 × 2 + 4 = 12 + 4 = 16
Fourth term = Third term × 3 + 3^{2}
⇒ Fourth term = 16 × 3 + 9 = 57
Fifth term = Fourth term × 4 + 4^{2}
⇒ Fifth term = 49 × 4 + 16 = 244
Hence , the place value of ( d ) is 244 .

10 11 15 24 40 6 (a) (b) (c) (d) (e) What will come in place of (c) ?

 14
 13
 12
 10
 None of these

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As per the details in the question the series is in the form of
First series :
First term = 10
Second term = First term + 1^{2} = 10 + 1 = 11
Third term = Second term + 2^{2} = 11 + 4 = 15
similarly , we can calculate the all next terms .
Second series :
First term = 6
Second term = First term + 1^{2} = 6 + 1 = 7
Third term = Second term + 2^{2} = 7 + 4 = 11Correct 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 + 1^{2}
⇒ Second term = 10 + 1^{2} = 10 + 1 = 11
Third term = Second term + 2^{2}
⇒ Third term = 11 + 2^{2} = 11 + 4 = 15
similarly , we can find the all others terms .
Second series :
First term = 6
Second term = First term + 1^{2}
⇒ Second term = 6 + 1^{2} = 6 + 1 = 7
Third term = Second term + 2^{2}
⇒ Third term = 7 + 2^{2} = 7 + 4 = 11
Fourth term = Third term + 3^{2}
⇒ Fourth term = 11 + 3^{2} = 11 + 9 = 20
Hence , the place value of ( c ) is 20 .

12 26 11 36 9 7 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c) ?

 7
 21
 4
 11
 None of these

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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 = 6Correct 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.

4 5 22 201 12 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (d) ?

 4948
 4840
 4048
 4984
 None of these

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