## Number Series

*A*number series is a group of numbers related to one another in a particular manner or pattern. There could be multiple patterns of relationship in the series such as:

1. the numbers are multiple of some number

e.g. 3, 6, 9, 12, 15...

2. the numbers may be consecutive odd/even numbers.

e.g. 5, 7, 9, 11, 13...

3. the numbers may be consecutive prime numbers.

4. the numbers may be squares of some numbers.

5. the subsequent numbers can be obtained by adding/multiplying/squaring etc. of previous number(s) in the series.

**Exercise****1. Find out the number that will come next in the series:**

*17, 19, 23, 29, 31, ?*

(a) 33

(b) 35

(c) 37

(d) 39

Answer: (c) 37

In the series the numbers are consecutive primes.

**2. Find out the number that will come next in the series:**

*9, 18, 27, 36, 45, ?*

(a) 53

(b) 54

(c) 58

(d) 63

**3. Find out the number that will come next in the series:**

*1, 8, 27, 64, 125...*

(a) 156

(b) 188

(c) 200

(d) 216

**4. Find out the number that will come next in the series:**

*9, 27, 0 , 64, ? , 155*

(a) -61

(b) 83

(c) -23

(d) 47

**5. Find out the number that will come next in the series:**

*10, 40, 90, 160, ?*

(a) 200

(b) 230

(c) 250

(d) 280

**6. Find out the number that will come next in the series:**

*2, 5, 11, 23, ?*

(a) 34

(b) 42

(c) 36

(d) 47

Answers:

2: (b) 54

Numbers are multiple of 9.

9 × 1 = 9, 9 × 2 = 18, 9 × 3 = 27...

3: (d) 216

Numbers are cube series i.e. 1³, 2³, 3³, 4³...

4: (a) 61

19 + 2³ = 27

27 - 3³ = 0

0 + 4³ = 64

64 - 5³ = -61

-61 + 6³ = 155

5: (c) 250

Numbers are multiples of 10 ⇒ 1 × 10 = 10, 2 × 20 = 40, 3 × 30 = 90, 4 × 40 = 160...

6: (d) 47

2 × 2 + 1 = 5,

5 × 2 + 1 = 11,

11× 2 + 1 = 23

23× 2 + 1 = 47