1. Find the missing term: 6, 18, 3, 21, 7, 56, ?

a) 8

b) 9

c) 63

d) 64

Explanation: Each term at an even place in the series is the product of its two adjacent terms.

Thus, if the missing term be x, then we have :

7 × x = 56 or x = 56 ÷ 7 = 8

2. Find the missing term: 1, 3, 4, 8, 15, 27, ?

a) 37

b) 44

c) 50

d) 55

Explanation: The sum of any three consecutive terms of the series gives the next term,

So, missing number = 8 + 15 + 27 = 50

3. Find the missing term: 20, 20, 19, 16, 17, 13, 14, 11, ?, ?

a) 10, 10

b) 10, 11

c) 13, 14

d) 13, 16

Explanation: Let the missing terms of the series be x

_{1}and x

_{2}.

Thus, the sequence 20, 20, 19, 16, 17, 13, 14, 11. x

_{1}, x

_{2}is a combination of two series:

I. 20, 19, 17, 14, x

_{1}and

II. 20, 16, 13, 11, x

_{2}

The pattern in I is - 1, - 2, - 3,..............So, missing term, x

_{1}= 14 - 4 = 10

The pattern in II is - 4, - 3, - 2,.......... So,missing term, x

_{2}= 11 - 1 = 10

4. Find the missing term: 45, 54, 47, ?, 49, 56, 51, 57, 53

a) 48

b) 50

c) 55

d) None of these

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

I. 45, 47, 49, 51, 53 and

II. 54, ?, 56, 57

Clearly, II. consists of consecutive natural numbers, starting from 54.

so, missing term = 55.

5.Find the missing term: 2, 15, 4, 12, 6, 7, ?, ?

a) 8, 8

b) 8, 0

c) 3, 8

d) None of these

Explanation: Let the missing terms of the series be x

_{1}and x

_{2}.

Thus, the sequence 2, 15, 4, 12, 6, 7, x

_{1}, x

_{2}is a combination of two series:

I. 2, 4, 6, x

_{1}and

II. 15, 12, 7, x

_{2}

I consists of consecutive even numbers. So, missing term, x

_{1}= 8

The pattern in II is - 3, - 5, ........So, missing term x

_{2}= 7 - 7 = 0

6. Find the missing number: 11^{1}/_{9}, 12^{1}/_{2}, 14^{2}/_{7}, 16^{2}/_{3}, ?

a) 8^{1}/_{3}

b) 19^{1}/_{2}

c) 20

d) 22^{1}/_{3}

Explanation: The given sequence is

^{100}/

_{9},

^{25}/

_{2},

^{100}/

_{7},

^{50}/

_{3}, ............i.e.,

^{100}/

_{9},

^{100}/

_{8},

^{100}/

_{7},

^{100}/

_{6}.................

So, missing term =

^{100}/

_{5}= 20

7. Find the missing term: 8, 9, 8, 7, 10, 9, 6, 11, 10, ?, 12

a) 5

b) 7

c) 8

d) 11

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

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

II. 2nd, 5th, 8th, 11th terms i.e.,9, 10, 11, 12

III. 3rd, 6th, 9th, terms i.e., 8, 9, 10

The pattern in I. is - 1 So, the missing term is = 6 - 1 = 5

8. Which term of the series 5, 8, 11, 14, ....is 320 ?

a) 104th

b) 105th

c) 106th

d) 64th

Explanation: Clearly, 5 + 3 = 8, 8 + 3 = 11, 11 + 3 = 14,................

So, the series in an A.P. in which a = 5 and d = 3

Let 320 be the nth term of the series.

Then, 320 = 5 + (n - 1) × 3 or (n - 1) = 105 or n = 106

9. Find the missing term: 1, 9, 25, 49, ?, 121

a) 64

b) 81

c) 91

d) 100

Explanation: The given series consists of squares of consecutive odd numbers i.e., 1

^{2}, 3

^{2}, 5

^{2}, 7

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

So. missing term = 9

^{2}= 81

10. Find the missing term: 4, 6, 9, 13^{1}/_{2}, ?

a) 17^{1}/_{2}

b) 19

c) 20^{1}/_{4}

d) 22^{3}/_{4}

Explanation: The pattern is ×

^{3}/

_{2}.

So, missing number = 13

^{1}/

_{2}×

^{3}/

_{2}=

^{27}/

_{2}×

^{3}/

_{2}=

^{81}/

_{4}= 20

^{1}/

_{4}.