Question 1

25 146 65 114 39 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (e)?

Accepted Answer

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).

Question 2

1, 2, 4.5, 11, 30, 92.5, 329

Accepted Answer

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.

Question 3

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

Accepted Answer

The Order of above given series is First term + Second term = Third term ⇒ 2 + 5 = 7; Second term + Third term = Fourth term ⇒ 5 + 7 = 12; Third term + Fourth term = Fifth term ⇒ 7 + 12 = 19;... Fourth term + Fifth term = Sixth term ⇒ 12 + 19 = 32 , 31 should be 6th term because 12 + 19 = 31 So 32 is wrong. we get 31 as 6th term. Fifth term + Sixth term = Seventh term ⇒ 19 + 31 = 50

Question 4

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 5

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 6

–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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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 20

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

Number Series Questions