2, 5, 7, 12, 19, 32, 50

Correct Answer: 92.5

Explanation:

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.

Correct Answer: 112

Explanation:

The given series is in the below pattern ,
First series :-
First term = 25
Second term = First term + 11²
? Second term = 25 + 11² = 25 + 121 = 146
Third term = Second term - 9²
? Third term = 146 - 9² = 146 - 81 = 65
similarly , we can calculate the all next terms .
Second series :-
First term = 39
Second term = First term + 11²
? Second term = 39 + 11² = 39 + 121 = 160
Third term = Second term - 9²
? Third term = 160 - 9² = 160 - 81 = 79
Fourth term = Third term + 7²
? Fourth term = 79 + 7² = 79 + 49 = 128
Fifth term = Fourth term - 5²
? Fifth term = 128 - 5² = 128 - 25 = 103
Fifth term = Fourth term - 5²
? Sixth term = 103 + 3² = 103 + 9 = 112
So 112 should come in place of (e).

Correct Answer:

Explanation:

The given series is in the below pattern ,
First series :-
First term = 4
Second term = First term × 1² + 1
? Second term = 4 × 1² + 1 = 4 + 1 = 5
Third term = Second term × 2² + 2
? Third term = 5 × 2² + 2 = 20 + 2 = 22
similarly , we can calculate the all next terms .
Second series :-
First term = 12
Second term = First term × 1² + 1
? Second term = 12 × 1² + 1 = 12 + 1 = 13
Third term = Second term × 2² + 2
? Third term = 13 × 2² + 2 = 52 + 2 = 54
Fourth term = Third term × 3² + 3
? Fourth term = 54 × 3² + 3 = 486 + 3 = 489
Fifth term = Fourth term × 4² + 4
? Fifth term = 489 × 4² + 4 = 7824 + 4 = 7828
Hence , the place value of ( d ) is 7828 .

Correct Answer: 21

Explanation:

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.

Correct Answer:

Explanation:

As per the details in the question the series is in the form of
First series :-
First term = 10
Second term = First term + 1²
? Second term = 10 + 1² = 10 + 1 = 11
Third term = Second term + 2²
? Third term = 11 + 2² = 11 + 4 = 15
similarly , we can find the all others terms .
Second series :-
First term = 6
Second term = First term + 1²
? Second term = 6 + 1² = 6 + 1 = 7
Third term = Second term + 2²
? Third term = 7 + 2² = 7 + 4 = 11
Fourth term = Third term + 3²
? Fourth term = 11 + 3² = 11 + 9 = 20
Hence , the place value of ( c ) is 20 .

Correct Answer: 3002

Explanation:

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.

Correct Answer: 124

Explanation:

The given series is in the below pattern,we can see that
Next term ( T_n ) = n³ - 1 { where , putting n = 1 , 2 , 3 , 4 , 5 respectively }
First term = T₁ = 1³ - 1 = 0
Second term = T₂ = 2³ - 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

Correct Answer: 3

Explanation:

The number pattern is described in the below image.
As per figure we can see the number series is in specific pattern which will help us to find the next number.
It is clear that we are getting the next terms on adding + 1 , + 3 , + 5 , + 7 , + 9 in previous term respectively.
First term = - 1
Second term = First term + 1
? Second term = -1 + 1 = 0
Third term = Second term + 3
? Third term = 0 + 3 = ( ? )
? ( ? ) = 3
Similarly we can calculate the all others terms
? Fourth term = 8
? Fifth term= 15

Correct Answer: 120

Explanation:

As per given series , we can see that
First term = 1
Second term = First term × 2
? Second term = 1 × 2 = 2
Similarly we can find the all others terms
Third term = Second term × 3
? Third term = 2 × 3 = 6
Fourth term = Third term × 4
? Fourth term = 6 × 4 = 24
Fifth term = Fourth term × 5
? Fifth term = 24 × 5 = ?
? ? = 120
Sixth term = Fifth term × 6
? Sixth term = 120 × 6 = 720

Correct Answer: 16

Explanation:

The given series is in the below pattern,we can see that
Square root of ( First term - Third term ) = Second term
? Square root of ( 251 ? 107 ) = Square root of 144 = 12 = Second term
Square root of ( Fourth term - sixth term ) = Fifth term
? 381 ? 125 = Square root of 256 = 16 = Fifth term
? Fifth term ( ? ) = 16
Hence, 16 is the missing number in the given question.