1. Find the missing term: 5, 2, 7, 9, 16, 25, ?

a) 41

b) 45

c) 48

d) 52

Explanation: Each term in the series, except the first two terms, is the sum of the preceding two terms.

So, missing term = 16 + 25 = 41

2. Find the missing term: 1, 1, 4, 8, 9, 27, 16, ?

a) 32

b) 64

c) 81

d) 256

Explanation: The series consists of squares and cubes of consecutive natural numbers i.e., 1

^{2}, 1

^{3}, 2

^{2}, 2

^{3}, 3

^{2}, 3

^{3}, 4

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

So, missing term = 4

^{3}= 64

3. Find the missing term: 10, 14, 26, 42, 70, ?

a) 100

b) 102

c) 106

d) 114

Explanation: Each term in the series, except the first two terms, is 2 more than the sum of the preceding two terms.

So, missing term = (42 + 70) +2 = 114

4. Find the missing term: 4, 12, 36, 108, ?

a) 144

b) 216

c) 304

d) 324

Explanation: The pattern is × 3

So, missing term = 108 × 3 = 324

5. Find the missing term: 2, 8, 16, 128, ?

a) 2042

b) 2046

c) 2048

d) 2056

Explanation: Each term in the series, except the first two terms, is the product of the preceding two terms.

So, missing term = 16 × 128 = 2048

6. Find the missing term: 3, 4, 7, 7, 13, 13, 21, 22, 31, 34, ?

a) 42

b) 43

c) 51

d) 52

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

I. 3, 7, 13, 21, 31, ? and

II. 4, 7, 13, 22, 34

The pattern in I is + 4, + 6, + 8, + 10,......

The pattern in II is + 3, + 6, + 9, + 12,..............

So, missing term = 31 + 12 = 43

7. Find the missing term : 90, 180, 12, 50, 100, 200, ?, 3, 50, 4, 25, 2, 6, 30, 3

a) 150

b) 175

c) 225

d) 250

Explanation: Clearly, 90 = 30 × 3, 180 = 6 × 30, 12 = 2 × 6, 50 = 25 × 2, 100 = 4 × 25, 200 = 50 × 4

So, missing term = 3 × 50 = 150

8. In the series 10, 17, 24, 31, 38,...... which of the following will be a number of the series ?

a) 48

b) 346

c) 574

d) 1003

Explanation: The given series consists of numbers each of which, on dividing by 7, leaves a remainder 3, No other number except 346 satisfies the property.

9. Find the missing term: 13, 32, 24, 43, 35, ?, 46, 65, 57, 76

a) 45

b) 52

c) 54

d) 55

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

I. 13, 24, 35, 46, 57 and

II. 32, 43, ?, 65, 76

The pattern in both I and II is + 11

So, missing term = 43 + 11 = 54

10. Find the missing term: ^{4}/_{9}, ^{9}/_{20}, ? , ^{39}/_{86}

a) ^{17}/_{40}

b) ^{19}/_{42}

c) ^{20}/_{45}

d) ^{29}/_{53}

Explanation: The sequence in the numerators is + 5, + 10, + 20, ......and that in the denominators is + 11, + 22, + 44,............

So, the numerator of the missing fraction should be (9 + 10)i.e., 19 and the denominator should be (20 + 22)i.e., 42. Thus, the missing term is

^{19}/

_{42}.