1. Find the missing term: 0, 4, 6, 3, 7, 9, 6, ?, 12

a) 8

b) 10

c) 11

d) 14

Explanation: The given sequence is a combination of three series:

I. 0, 3, 6

II. 4, 7, ?

III. 6, 9, 12

The pattern in each of these series is + 3

So, missing term = 7 + 3 = 10

2. In the series 3, 9, 15,.............what will be the 21st term?

a) 117

b) 121

c) 123

d) 129

Explanation: Clearly, 3 + 6 = 9, 9 + 6 = 15,.............

So, the series is an A.P in which a = 3 and d = 6

∴21st term = a + (21 - 1)d = a + 20d

= 3 +20 × 6 = 123.

3. Find the missing number: ^{2}/_{√5}, ^{3}/_{5}, ^{4}/_{5√5}, ^{5}/_{25}, ?

a) ^{6}/_{5√5}

b) ^{6}/_{25√5}

c) ^{6}/_{125}

d) ^{7}/_{25}

Explanation: Clearly, the numerators of the given fractions are consecutive natural numbers. So, the numerator of the missing fraction should be 6. Also, the denominator of each fraction is multiplied by √5 to obtain the denominator of the next fraction. So. the denominator of the missing fraction should be 25√5. Hence,the missing term is

^{6}/

_{25√5}

4. In the series 2, 6, 18, 54, ...., what will be the 8th term ?

a) 4370

b) 4374

c) 7443

d) 7434

Explanation: Clearly, 2 × 3 = 6, 6 × 3 = 18, 18 × 3 = 54,..............

S, the series is a G.P. in which a = 2, r = 3

∴8th term = ar

^{(8 - 1)}= ar

^{7}= 2 × 3

^{7}= (2 × 2187) = 4374

5. Find the missing term: 2, 1, 2, 4, 4, 5, 6, 7, 8, 8, 10, 11, ?

a) 9

b) 10

c) 11

d) 12

Explanation: The given sequence is a combination of three series:

I. 1st, 4th, 7th, 10th, 13th terms i.e., 2, 4, 6, 8, ?

II. 2nd, 5th, 8th, 11th terms i.e., 1, 4, 7, 10

III. 3rd, 6th, 9th, 12th terms i.e., 2, 5, 8, 11

Clearly, I. consists of consecutive even numbers. So, the missing term is 10.

6. Find out the wrong term: 0, 2, 3, 5, 8, 10, 15, 18, 24, 26, 35

a) 18

b) 24

c) 26

d) 10

Explanation: The given sequence is a combination of two series:

I. 0, 3, 8, 15, 24, 35 and II. 2, 5, 10, 18, 26

The pattern in both I and II is + 3, + 5, + 7, + 9, .........

So, in II. 18 is wrong and must be replaced by (10 + 7) i.e., 17.

7. Find out the wrong term: 196, 169, 144, 121, 101

a) 101

b) 121

c) 169

d) 196

Explanation: The sequence is (14)

^{2}, (13)

^{2}, (12)

^{2}, (11)

^{2}, (10)

^{2}..........

So, 101 is wrong and must be replaced by (10)

^{2}i.e., 100

8. Find out the wrong term: 2, 5, 10, 50, 500, 5000

a) 5

b) 10

c) 50

d) 5000

Explanation: Each term of the series is the product of the preceding two terms.

So, 5000 is wrong and must be replaced by (50 × 500) = i.e., 25000

9. Find out the wrong term: 5, 27, 61, 122, 213, 340, 509

a) 27

b) 61

c) 122

d) 509

Explanation: We have :

I: 5 27 61 122 213 340 509

II: 22 34 61 91 127 169

III: 12 27 30 36 42

IV: 15 3 6 ; 6

Clearly, the given series becomes a triangular pattern series if each term in IV: is 6.

Again, in II: 34 must be replaced by (61 - 24) i.e., 37 and 22 by (37 - 18) i.e., 19.

Thus, in the given series, 27 is wrong and must be replaced by (5 + 19) i.e., 24.

10. Find out the wrong term:3, 10, 27, 4, 16, 64, 5, 25, 125

a) 3

b) 4

c) 10

d) 27

Explanation: The correct sequence is 3, 3

^{2}, 3

^{3},4, 4

^{2}, 4

^{3},5, 5

^{2}, 5

^{3}

So. 10 is wrong and must replaced by 3

^{2}i.e., 9