Question 1

2, 14, 91, 546, 3002, 15015

Accepted Answer

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.

Question 2

0, 7, 26, 63,?

Accepted Answer

The given series is in the below pattern,we can see that Next term ( Tn ) = 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

Question 3

–1, 0,?, 8, 15, 24

Accepted Answer

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

Question 4

1, 2, 6, 24,? ,720

Accepted Answer

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

Question 5

251, (12), 107, 381, (?) , 125

Accepted Answer

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.

Question 6

3120,?, 122, 23, 4

Accepted Answer

As per above given series , we can see that Descending order of given series - Next term = ( 5 x previous term ) + odd number ( which starts 3 ) Here , 5th term = 4 4th term = 5 × 5th term + 3 ⇒ 4th term = 5 × 4 + 3 = 23 3rd term= 5 × 4th term + 7 ⇒ 3rd term= 5 × 23 + 7 = 122 Similarly , we can find all others terms also. 2nd term = 5 × 3rd term + 11 ⇒ 2nd term = 5 × 122 + 11 = ? ⇒ ? = 621 1st term = 5 × 2nd term + 15 ⇒ 1st term = 5 × 621 + 15 =3120

Question 7

7, 4, 5, 9, 20, 51, 106.5

Accepted Answer

The series is x 0.5 + 0.5, x 1 + 1, x 1.5 + 1.5. x 2 + 2, x 2.5 + 2.5, x 3 +3

Question 8

18, 20, 23, 32, 48, 73, 109

Accepted Answer

The series is 18 +12 = 19; 19 + 22 = 23; 23 + 32 = 32; 32 + 42 = 48; 48 + 52 = 73 + 62 = 109

Question 9

3, 7, 16, 35, 72, 153, 312

Accepted Answer

The series is x 2 + 1, x 2 + 2, x 2 + 3, x 2 + 4, x 2 + 5

Question 10

2, 7, 30, 138, 524, 1557, 3102

Accepted Answer

(2 - 1) x 7 = 7; (7 - 2) x 6 = 30; (30 - 3) x 5 = 135; (135 - 4) x 4 = 524; (524 - 5) x 3 = 1557; (1557 - 6) x 2 = 3102

Question 11

6, 10, 14, 34, 66, 130, 258

Accepted Answer

The series is x 2 - 2, x 2 - 2, x 2 - 2, x 2 - 2, ......

Question 12

1, 3, 10, 21, 64, 129, 356, 777

Accepted Answer

Pattern is x 2 + 1, x 3 + 1, x 2 + 1, x 3 + 1, ........

Question 13

3, 4, 10, 32, 136, 685, 4116

Accepted Answer

Pattern is : x 1 + 1, x 2 + 2, x 3 + 3, x 4 + 4, ............

Question 14

380, 188, 92, 48, 20, 8, 2

Accepted Answer

Pattern is : - 192, - 96, - 48, - 24, -12, - 6

Question 15

4, 10, 22, 46, 96, 190, 382

Accepted Answer

Pattern is : + 6, + 12, + 24, + 48, +96, + 192

Question 16

2, 3, 4, 4, 6, 8, 9, 12, 16

Accepted Answer

Pattern is : the series is the combination of three series -each term is twice the preceding term. (i) 1st, 4st, 7st term i. e 2,4,9,....... (ii) 2st, 5st, 8st term i, e 3,6,12..... (iii) 3st, 6st, 9st 4,8,16...... So, 9 is wrong.

Question 17

4, 28, 160, 990, 6970,55832, 502560

Accepted Answer

4 x 4 + (4 x 3) = 28 28 x 5 + (5 x 4) =160 160 x 6 + (6 x 5) = 990 990 x 7 + (7 x 6) = 6972 6972 x 8 + (8 x 7) = 55832 55832 x 9 + (9 x 8) = 502560

Question 18

13, 14, 27, 45, 68, 109, 177

Accepted Answer

13 + 14 = 27 14 + 27 = 41 27 + 41 = 68 41 + 68 = 109 68 + 109 = 117 So, 45 is the wrong number in this series.

Question 19

529, 841, 961, 1296, 1681, 1849, 2209

Accepted Answer

All nos, in the given series are squeres of odd nos, except 1296 1296 = (36)2

Question 20

1 , 3 , 4 , 7 , 11 ,18 , 27 , 47

Accepted Answer

As per the details in the question the series is in the form of The sum of the first two nos. is the third no. ∴ First term + Second term = Third term ⇒ 1 + 3 = 4 ; Second term + Third term = Fourth term ⇒ 3 + 4 = 7 ; Third term + Fourth term = Fifth term ⇒ 4 + 7 = 11 ; Fourth term + Fifth term = Sixth term ⇒ 7 + 11 = 18 ; Fifth term + Sixth term = Seventh term ⇒ 11 + 18 = 27 is wrong. It should be 29. Sixth term + Seventh term = Eighth term ⇒ 18 + 29 = 47 Hence, 27 is wrong. It should be 29.

Number Series Questions