Question 1

4 9 25 103 3 (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 = 4 Second term = First term × 2 + 1 ⇒ Second term = 4 × 2 + 1 = 9 Third term = Second term × 3 - 2 ⇒ Third term = 9 × 3 - 2 = 25 similarly , we can find the all others terms . ......... and so on . Second series :- First term = 3 Second term = First term × 2 + 1 ⇒ Second term = 3 × 2 + 1 = 7 Third term = Second term × 3 - 2 ⇒ Third term = 7 × 3 - 2 = 19 Fourth term = Third term × 4 + 3 ⇒ Fourth term = 19 × 4 + 3 = 79 Hence , the place value of ( c ) is 79 .

Question 2

6 10 32 126 2 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (a)?

Accepted Answer

The given series is in the below pattern , First series :- First term = 6 Second term = First term × 2 - 2 ⇒ Second term = 6 × 2 - 2 = 10 Third term = Second term × 3 + 2 ⇒ Third term = 10 × 3 + 2 = 32 similarly , we can find the all others terms . ......... and so on . Second series :- First term = 2 Second term = First term × 2 - 2 ⇒ Second term = 2 × 2 - 2 = 2 Hence , the place value of ( a ) is 2 .

Question 3

7 4 5 9 20 52.5 3 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c)?

Accepted Answer

As per the details in the question the series is in the form of First series :- First term = 7 Second term = First term × 0.5 + 0.5 ⇒ Second term = 7 × 0.5 + 0.5 = 4 Third term = Second term × 1 + 1 ⇒ Third term = 4 × 1 + 1 = 5 similarly , we can find the all others terms . Second series :- First term = 3 Second term = First term × 0.5 + 0.5 ⇒ Second term = 3 × 0.5 + 0.5 = 2 Third term = Second term × 1 + 1 ⇒ Third term = 2 × 1 + 1 = 3 Fourth term = Third term × 1.5 + 1.5 ⇒ Fourth term = 3 × 1.5 + 1.5 = 6 Hence , the place value of ( c ) is 6 .

Question 4

3 12 30 66 138 282 7 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (b)?

Accepted Answer

As per the details in the question the series is in the form of First series :- First term = 3 Second term = First term × 2 + 6 ⇒ Second term = 3 × 2 + 6 = 12 Third term = Second term × 2 + 6 ⇒ Third term = 12 × 2 + 6 = 30 similarly , we can find the all others terms . Second series :- First term = 7 Second term = First term × 2 + 6 ⇒ Second term = 7 × 2 + 6 = 20 Third term = Second term × 2 + 6 ⇒ Third term = 20 × 2 + 6 = 46 Hence , the place value of ( b ) is 46 .

Question 5

2 3 7 25 121 721 3 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c)?

Accepted Answer

The series is × 2 –1, × 3 – 2, × 4 – 3,..... The given series is in the below pattern , First series :- First term = 2 Second term = First term × 2 - 1 ⇒ Second term = 2 × 2 - 1 = 3 Third term = Second term × 3 - 2 ⇒ Third term = 3 × 3 - 2 = 7 similarly , we can calculate the all next terms . Second series :- First term = 3 Second term = First term × 2 - 1 ⇒ Second term = 3 × 2 - 1 = 5 Third term = Second term × 3 - 2 ⇒ Third term = 5 × 3 - 2 = 13 Fourth term = Third term × 4 - 3 ⇒ Fourth term = 13 × 4 - 3 = 49 Hence , the place value of ( c ) is 49 .

Question 6

1 8 10 35 136 2 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c)?

Accepted Answer

As per the details in the question the series is in the form of First series :- First term = 1 Second term = First term × 1 + 7 ⇒ Second term = 1 × 1 + 7 = 8 Third term = Second term × 2 - 6 ⇒ Third term = 8 × 2 - 6 = 10 similarly , we can find the all others terms . Second series :- First term = 2 Second term = First term × 1 + 7 ⇒ Second term = 2 × 1 + 7 = 9 Third term = Second term × 2 - 6 ⇒ Third term = 9 × 2 - 6 = 12 Fourth term = Third term × 3 + 5 ⇒ Fourth term = 12 × 3 + 5 = 41 Hence , the place value of ( c ) is 41 .

Question 7

9 19.5 41 84.5 12 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (c)?

Accepted Answer

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).

Question 8

38 19 28.5 71.25 18 (a) (b) (c) (d) (e) Which of the following numbers will come in place of (d)?

Accepted Answer

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).

Question 9

2, 13, 65, 271, 817, 1639, 1645

Accepted Answer

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.

Question 10

3, 4, 16, 75, 366, 1945, 11886

Accepted Answer

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

Question 11

6, 7, 18, 63, 265, 1365

Accepted Answer

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

Question 12

5, 4, 9, 18, 66, 195

Accepted Answer

This series is made of two position series . Even Position series :- ∴ First term = 5 Second term = ( First term × 1 ) - 1 ⇒ Second term = ( 5 × 1 ) - 1 = 4 Fourth term = ( Third term × 2 ) - 2 ⇒ Fourth term = ( 9 × 2 ) - 2 = 18 , 16 should be Fourth term because ( 9 × 2 ) - 2 = 16 . So 18 is wrong. we get 16 as Fourth term. Sixth term = ( Fifth term × 3 ) - 3 ⇒ Sixth term = ( 66 × 3 ) - 3 = 195 Odd Position series - ∴ Second term = 4 Third term = ( Second term × 2 ) + 2 ⇒ Third term = ( 4 × 2 ) + 2 = 10 Fifth term = ( Fourth term × 3 ) + 3 ⇒ Fifth term = ( 16 × 3 ) + 3 = 51

Question 13

2, 7, 28, 146, 877, 6140

Accepted Answer

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

Question 14

1, 2, 8, 21, 88, 445

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 ⇒ 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

Question 15

7, 23, 58, 127, 269, 555

Accepted Answer

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

Question 16

156, 506,?, 1806

Accepted Answer

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

Question 17

2, 5, 10, 19, 36,?

Accepted Answer

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

Question 18

2, 3, 6, 7, 14, 15,?

Accepted Answer

See the graph and found that the given number in the series with specific pattern. From the given graph , we can see that the increasing order of series as - First term = 2 Second term = First term + 1 = 2 + 1 = 3 , Third term = Second term x 2 = 3 x 2 = 6 , Fourth term = Third term + 1 = 6 + 1 = 7 , Fifth term = Fourth term x 2 = 7 x 2 = 14 , Sixth term = Fifth term + 1 = 14 + 1 = 15 , Seventh term = Sixth term x 2 = 15 x 2 = 30 ∴ Seventh term( ? ) = 30

Question 19

BCFG, JKNO, RSVW ,?

Accepted Answer

According to position of alphabets in alphabet table , we have B C F G → 2 , 3 ,6 , 7 J K N O → 10 , 11 , 14 , 15 R S V W → 18 , 19 , 22 , 23 { ∴ Next sequence = Adding 8 in every position of previous sequence alphabets } Next sequence = 18 + 8 , 19 + 8 , 22 + 8 , 23 + 8 Next sequence = 26, 27, 30, 31 = 26, 27 - 26 = 1, 30 - 26 = 4, 31 - 26 = 5 = Z A D E ( subtract the excess value by 26 ) We get , 26 , 1 , 4 , 5 → Z A D E = ( ? ) .

Question 20

0, 5, 60, 615,?

Accepted Answer

From given figure , it is clear that the increasing order of series given as - First term = 0 Second term = First term + 5 ⇒ Second term = 0 + 5 = 5 Third term = Second term + 55 ⇒ Third term = 5 + 55 = 60 Similarly , we can find all others terms also. Fourth term = Third term + 555 ⇒ Fourth term = 60 + 555 = 615 Fifth term = Fourth term + 5555 ⇒ Fifth term = 615 + 5555 = ? ∴ Fifth term ( ? ) = 6170

Number Series Questions