5, 4, 9, 18, 66, 195

Correct Answer:

Explanation:

The given series is in the below pattern,
First term = 6
Second term = First term x 1 +1²
? Second term = 6 x 1 + 1² = 6 + 1 = 7
Third term = Second term x 2 + 2²
? Third term = 7 x 2 + 2² = 14 + 4 = 18
Fourth term = Third term x 3 + 3²
? Fourth term = 18 x 3 + 3² = 54 + 9 = 63
Fifth term = Fourth term x 4 +4²
? Fifth term = 63 x 4 + 4² = 252 + 16 = 265
So 265 is wrong. we get 268 as 5th term.
Sixth term = Fifth term x 5 + 5²
? Sixth term = 268 x 5 + 5² = 1340 + 25 = 1365

Correct Answer: 366

Explanation:

The given series is in the below pattern,
First term = 3
Second term = First term x 1 +1³
? Second term = 3 x 1 + 1³ = 3 + 1 = 4
Third term = Second term x 2 + 2³
? Third term = 4 x 2 + 2³ = 8 + 8 = 16
Fourth term = Third term x 3 + 3³
? Fourth term = 16 x 3 + 3³ = 48 + 27 = 75
Fifth term = Fourth term x 4 +4³
? Fifth term = 75 x 4 + 4³ = 300 + 64 = 364
So 366 is wrong. we get 364 as 5th term.
Sixth term = Fifth term x 5 + 5³
? Sixth term = 364 x 5 + 5³ = 1820 + 125 = 1945
Seventh term = Sixth term x 6 + 6³
? Seventh term = 1945 x 6 + 6³ = 11670 + 216 = 11886

Correct Answer: 65

Explanation:

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.

Correct Answer: 118.125

Explanation:

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).

Correct Answer:

Explanation:

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).

Correct Answer: 341

Explanation:

As per the details in the question the series is in the form of
First term = 2
Second term = ( First term × 3 ) + 1
? Second term = ( 2 × 3 ) + 1 = 7
Third term = ( Second term × 4 ) + 1
? Third term = ( 7 × 4 ) + 1 = 28 is wrong , 29 should be sixth term because ( 7 × 4 ) + 1 = 29 .
So 28 is wrong. we get 29 as Third term.
Fourth term = ( Third term × 5 ) + 1
? Fourth term = ( 29 × 5 ) + 1 = 146
Fifth term = ( Fourth term × 6 ) + 1
? Fifth term = ( 146 × 6 ) + 1 = 877

Correct Answer:

Explanation:

As per the details in the question the series is in the form of
First term = 1
Second term = ( First term × Variable ) + Variable
? Second term = ( 1 × 1 ) + 1 = 2
Third term = ( First term × Variable ) + Variable
? Third term = ( 2 × 2 ) + 2 = 8 , So 8 is wrong. we get 6 as Third term.
Similarly , we can find the all terms also.
Fourth term = ( 6 × 3 ) + 3 = 21
Fifth term = ( 21 × 4 ) + 4 = 88
Sixth term = ( 88 × 5 ) + 5 = 445

Correct Answer: 261

Explanation:

The order of above series is given as
First term = 7
Second term = ( First term x 2 ) +9
? Second term = ( 7 x 2 ) + 9 = 14 + 9 = 23
Third term = ( Second term x 2 ) +11
? Third term = ( 23 x 2 ) + 11 = 46 + 11 = 58 is wrong , 57 should be Third term because ( 23 × 2 ) + 11 = 57 .
Similarly we can find all others terms also.
Fourth term = ( Third term x 2 ) +13
? Fourth term = ( 57 x 2 ) +13
Fifth term = ( Fourth term x 2 ) +15
? Fifth term = ( 127 × 2 ) + 15 = 269
Sixth term = ( Fifth term x 2 ) +17
? Sixth term = ( 269 × 2 ) + 17 = 555

Correct Answer: 1056

Explanation:

From the above given series , we have
First term + 350 = Second term
? 156 + 350 = 506
Second term + 550 = third term
? 506 + 550 = ? ? ? = 1056
From the given figure , we get the value of third term ( ? ) = 1056
Third term + 550 = Fourth term
? 1056 + 750 = 1806

Correct Answer: 69

Explanation:

See the below image and you will find a pattern in which numbers are getting added for next number in the given series.
From the given figure , we get the value of sixth term ( ? ) = 69