Question 1

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 2

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 3

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.

Question 4

3 , 2 , 3 , 6 , 12 , 37.5 , 115.5

Accepted Answer

The given series is in the below pattern,we can see that Next term= ( Previous term × variable ) + variable First term = 3 Second term = ( First term × variable ) + 0.5 = ( 3 x 0.5 ) + 0.5 = 2 Third term = ( Second term × variable ) + 1 = ( 2 x 1 ) + 1 = 3 Similarly , we can calculate all others terms also. Fourth term = ( Third term × variable ) + 1.5 = ( 3 × 1.5 ) + 1.5 = 6 ; Fifth term = ( Fourth term × variable ) + 2 = ( 6 × 2 ) + 2 = 12 ; 12 is wrong. It should be 14. Sixth term = ( Fifth term × variable ) + 2.5 = (14 × 2.5 ) + 2.5 = 37.5 ; Seventh term = ( Sixth term × variable ) + 3 = ( 37.5 × 3 ) + 3 = 115.5 Hence, 12 is wrong. It should be 14.

Question 5

2 , 3 , 11 , 38 ,102 , 229 , 443

Accepted Answer

The given series is in the below pattern, First term = 2 Second term = First term + 13 ⇒ Second term = 2 + 13 = 3 ; Third term = Second term + 23 ⇒ Third term = 3 + 23 = 11 ; Similarly , we can find the all others terms also. Fourth term = Third term + 42 ⇒ Fourth term = 11 + 33 = 38 ; Fifth term = Fourth term + 52 ⇒ Fifth term = 38 + 43 = 102 Sixth term = Fifth term + 62 ⇒ Sixth term = 102 + 53 = 229 ; 229 is wrong. It should be 227. Seventh term = Sixth term + 72 ⇒ Seventh term = 227 + 63 = 443 Hence, 229 is wrong. It should be 227.

Question 6

2807, 1400, 697, 347, 171, 84, 41, 20

Accepted Answer

From the given figure , we can see that First term = 2807 Second term = ( First term - 7 ) ÷ 2 = 1400 Third term = ( Second term - 6 ) ÷ 2 = 697 ⇒ Second term = ( 2807 - 7 ) ÷ 2 = 1400 ; ⇒ Third term = ( 1400 - 6 ) ÷ 2 = 697 ; ⇒ Fourth term = ( 697 - 5 ) ÷ 2 = 347; 347 is wrong. It should be 346. ⇒ Fifth term = ( 346 - 4 ) ÷ 2 = 171 ; ⇒ Sixth term = ( 171 - 3 ) ÷ 2 = 84 ; ⇒ Seventh term = ( 84 - 2 ) ÷ 2 = 41 ; ⇒ Eighth term = ( 41 - 1 ) ÷ 2 = 20 Hence, 347 is wrong. It should be 346.

Question 7

2 , 3 , 5 , 8 , 14 , 23 , 41, 69

Accepted Answer

The series is an alternate series, having Odd position series :- First term = 2 Third term = ( First term × 3 ) - 1 ⇒ Third term = ( 2 × 3 ) - 1 = 5 ; Fifth term = ( Third term × 3 ) - 1 ⇒ Fifth term = ( 5 × 3 ) - 1 = 14 ; Seventh term = ( Fifth term × 3 ) - 1 ⇒Seventh term = ( 14 × 3 ) - 1 = 41 ; Even position series :- Second term = 3 Fourth term = ( Second term × 3 ) - 1 ⇒ Fourth term = ( 3 × 3 ) - 1 = 8 ; Sixth term = ( Fourth term × 3 ) - 1 ⇒ Sixth term = ( 8 × 3 ) - 1 = 23 ; Eighth term = ( Sixth term × 3 ) - 1 ⇒ Eighth term = ( 23 × 3 ) - 1 = 69; 69 is wrong. It should be 68.

Question 8

3 , 7. 5 ,15 , 37.5 , 75 ,167.5 , 375

Accepted Answer

The given series is in the below pattern, First term = 3 Second term = First term × 2.5 ⇒ Second term = 3 × 2.5 = 7.5 ; Third term = Second term × 2 ⇒ Third term = 7.5 × 2 = 15 ; Fourth term = Third term × 2.5 ⇒ Fourth term = 15 × 2.5 = 37.5 ; Fifth term = Fourth term × 2 ⇒ Fifth term = 37.5 × 2 = 75 ; Sixth term = Fifth term × 2.5 ⇒ Sixth term = 75 × 2.5 = 167.5; 167.5 is wrong. It should be 187.5. Seventh term = Sixth term × 2 ⇒ Seventh term = 187.5 × 2 = 375 ; Hence, 167.5 is wrong. It should be 187.5.

Question 9

36 , 20 , 12 , 8 , 6 , 5.5 , 4.5

Accepted Answer

As per given above series , it is clear that Difference between all terms are given as :- 16 ÷ 2 = 8 , 8 ÷ 2 = 4 , 4 ÷ 2 = 2 , 2 ÷ 2 = 1 , 1 ÷ 2 = 0.5 . First term = 36 Second term = First term - 16 ⇒ Second term = 36 - 16 = 20 ; Third term = Second term - 8 ⇒ Third term = 20 - 8 = 12 ; Similarly , we can find all others terms also. Fourth term = Third term - 4 = 12 - 4 = 8 ; Fifth term = Fourth term - 2 = 8 - 2 = 6 ; Sixth term = Fifth term - 1 = 6 - 1 = 5.5; 5.5 is wrong. It should be 5 . Seventh term = Sixth term - 0.5 = 5 - 0.5 = 4.5 Hence, 5.5 is wrong. It should be 5 as Sixth term .

Question 10

1, 3, 9, 31, 128, 651, 3913

Accepted Answer

As per the details in the question the series is in the form of Next term = ( Previous term × variable ) + ( 1 + variable ) First term = 1 Second term = First term × 1 + 2 ⇒ Second term = 1 × 1 + 2 = 3 ; Third term = Second term × 2 + 3 ⇒ Third term = 3 × 2 + 3 = 9 ; Similarly , we can find all others terms also. Fourth term = Third term × 3 + 4 ⇒ Fourth term = 9 × 3 + 4 = 31 ; Fifth term = Fourth term × 4 + 5 ⇒ Fifth term = 31 × 4 + 5 = 128 , is wrong . it should be 129 as fifth term . Sixth term = Fifth term × 5 + 6 ⇒ Sixth term = 129 × 5 + 6 = 651 ; Seventh term = Sixth term × 6 + 7 ⇒ Seventh term = 651 × 6 + 7 = 3913

Question 11

11 , 18 , 39 , 97.5 , 295.5 ,1037.75

Accepted Answer

As per the details in the question the series is in the form of Next term = Previous term × variable +variable First term = 11 Second term = First term × 1.5 + 1.5 ⇒ Second term = 11 × 1.5 + 1.5 = 18 ; Third term = Second term × 2 + 2 ⇒ Third term = 18 × 2 + 2 = 39 , is wrong . it should be 38 as third term . Similarly , we can find all others terms also. Fourth term = Third term × 2.5 + 2.5 ⇒ Fourth term = 38 × 2.5 + 2.5 = 97.5 ; Fifth term = Fourth term × 3 + 3 ⇒ Fifth term = 97.5 × 3 + 3 = 295.5 ; Sixth term = Fifth term × 3.5 + 3.5 ⇒ Sixth term = 295.5 × 3.5 + 3.5 = 1037.75 ; New series is given as - First term = 39 × 1.5 + 1.5 = 60; Second term = 60 × 2 + 2 = 122. Hence Second term of new series is 122.

Question 12

2 , 9 , 5 , 36 , 125 , 648 , 3861

Accepted Answer

As per the details in the question the series is in the form of First term = 2 Second term = First term × 1 + 7 ⇒ Second term = 2 × 1 + 7 = 2 + 7 = 9 ; Third term = Second term × 2 - 11 ⇒ Third term = 9 × 2 - 11 = 18 - 11 = 5; 5 is wrong. It should be 7 as Third term . Similarly , we can find all others terms also. Fourth term = Third term × 3 + 15 ⇒ Fourth term = 7 × 3 + 15 = 21 + 15 = 36 ; Fifth term = Fourth term × 4 - 19 ⇒ Fifth term = 36 × 4 - 19 = 144 -19 = 125 ; Sixth term = Fifth term × 5 + 23 ⇒ Sixth term = 125 × 5 + 23 = 625 + 23 = 648 ; Seventh term = Sixth term × 6 - 27 ⇒ Seventh term = 648 × 6 - 27 = 3888 - 27 = 3861 . New series is First term = 5 × 1 + 7 = 12; Second term = 12 × 2 - 11 = 13. Hence Second term of new series is 13 and correct option is ( E ) .

Question 13

2, 7, 19, 43, 99, 209, 431

Accepted Answer

The given series is in the below pattern, First term = 2 Second term = ( First term × 2 ) + 3 ⇒ Second term = ( 2 × 2 ) + 3 = 7 ; Third term = ( Second term × 2 ) + 5 ⇒ Third term = ( 7 × 2 ) + 5 = 19 Similarly , we can calculate all others terms also. Fourth term = ( Third term × 2 ) + 7 ⇒ Fourth term = ( 19 × 2 ) + 7 = 43 , is wrong.it should be 45 as fourth term . Fifth term = ( Fourth term × 2 ) + 9 ⇒ Fifth term = ( 45 × 2 ) + 9 = 99 ; Sixth term = ( Fifth term × 2 ) + 11 ⇒ Sixth term = ( 99 × 2 ) + 11 = 209 ; Seventh term = ( Sixth term × 2 ) + 11 ⇒ Seventh term = ( 209 × 2 ) + 13 = 431 New series is given as - First term = 43 × 2 + 3 = 89; Second term = 89 × 2 + 5 = 181. Hence Second term of new series is 181.

Question 14

1 , 2 , 6 , 33 ,148 , 765 , 4626

Accepted Answer

From above given series , we can see that Next term = Previous term × variable + variable2 First term = 1 Second term = First term × 1 + 12 ⇒ Second term = 1 × 1 + 12 = 1 + 1 = 2 ; Third term = Second term × 2 + 22 ⇒ Third term = 2 × 2 + 22 = 4 + 4 = 6; 6 is wrong. It should be 8. Here, 6 is the wrong number. Similarly , we can find all others terms also. Fourth term = Third term × 3 + 32 ⇒ Fourth term = 8 × 3 + 32 = 24 + 9 = 33 ; Fifth term = Fourth term × 4 + 42 ⇒ Fifth term = 33 × 4 + 42 = 132 + 16 = 148 ; Sixth term = Fifth term × 5 + 52 ⇒ Sixth term = 148 × 5 + 52 = 740 + 25 = 765 ; Seventh term = Sixth term × 6 + 62 ⇒ Seventh term = 765 × 6 + 62 = 4590 + 36 = 4626 . New series is given as :- First term = wrong term × 1 + 12 = 6 × 1 + 12 = 7; Second term = wrong term × 1 + 12 = 6 × 2 + 22 = 16. Hence Second term of new series is 16 .

Question 15

BYCXW, CXDWV, EVFUT, GTHSR,?

Accepted Answer

From given figure , it is clear that On adding 2 and subtracting 2 alternately in fourth term of given series . We get , The next term of above given series is IRJQP .

Question 16

QPO, SRQ, UTS, WVU, (?)

Accepted Answer

From given figure , it is clear that On adding 2 in Each letter of given series .We get , The next term of above given series is YXW. Hence the correct option will be B .

Question 17

AZ, CX, FU, (?)

Accepted Answer

The given series is in the below pattern, 1st letter moves +2, +3 and +4 steps respectively. 2nd letter moves –2, –3 and –4 steps respectively. Hence the place value of ? is JQ .

Question 18

OTE, PUF, QVG, RWH,?

Accepted Answer

As per the details in the question the series is in the form of The first letters of the terms are in alphabetical order, and so are the second and third letters. Hence required answer will be SXI .

Question 19

MHZ, NIW, OKT, PNQ,?

Accepted Answer

The first letters of the terms are consecutive letters. The third letter of each term is moved three steps backward to obtain the third letter of the successive term. The middle letters of the first, second, third and fourth terms are moved one, two, three, and four steps forward respectively to obtain the middle letter of the successive terms. The order of above series given as - + 1 , + 2 , - 3 MHZ, NIW, OKT, PNQ, ( ? ) So ? = QRN → 17 18 14 Hence , required answer will be QRN .

Question 20

6 3.0 4.5 2.25 4.0 12 40 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c)?

Accepted Answer

The given series is in the below pattern , First series :- First term = 6 Second term = First term ÷ 2 ⇒ Second term = 6 ÷ 2 = 3 Third term = Second term × 1.5 ⇒ Third term = 3 × 1.5 = 4.5 similarly , we can calculate the all next terms . ........... and so on. Second series :- First term = 40 Second term = First term ÷ 2 ⇒ Second term = 40 ÷ 2 = 20 Third term = Second term × 1.5 ⇒ Third term = 20 × 1.5 = 30 Fourth term = Third term ÷ 2 ⇒ Fourth term = 30 ÷ 2 = 15 Hence , the place value of (c) is 15 .

Number Series Questions