Chapter 2 SERIES
INTRODUCTION
A series is a sequence of numbers/alphabetical letters or both which follow a particular rule. Each element of series is called ‘term’. We have to analyse the pattern and find the missing term or next term to continue the pattern.
Types of series are explained in the following chart:
Number Series
A series that is made by only number or digit.
- Ascending series
- Descending series
- Oscillating series
Alphabet Series
A series that is made by only alphabetic letters.
Alpha-numeric Series
A series in which both alphabets and numbers are used.
Continuous Pattern Series
A series of letters, which follow a certain pattern, is given with four/five times blank
spaces in between. The order of missing letters is correct answer.
Mixed Series
A series which is created by the combination of two or more than two series.
Correspondence Series
A series consists of three sequence with
three different elements (for ex.capital letters, numbers and small letters). An element of each sequence is correspond to the element of other sequence on the basis of the similarity in position.
NUMBER SERIES
Number series is a form of numbers in
a certain sequence, where some numbers are mistakenly put into the series of numbers and some number is missing in that series, we need to observe first and then find the accurate number to that series of numbers.
Remember
· Even and odd numbers.
· Prime and composite numbers.
· Square and square roots of a numbers.
· Cube and cube roots of a numbers.
•Arithmetic Operations
- Addition
- Subtraction
- Division
- Multiplication
Types of Number Series
1.Perfect Square Series
This type of serics are based on square of a number which is in same order and one square number is missing in that given series.
EXAMPLE 841, ?, 2401, 3481, 4761
Sol. (29)^2, 39^2, 45^2, 59^2, 69^2
2. Perfect Cube Series
Perfect Cube series is an arrangement of numbers in a certain order, where some number which is in same order and one cube is missing in that given series.
EXAMPLE 4096, 4913, 5832, ?, 8000
Sol. 16^3, 17^3, 18^3, 19^3, 20^3
3. Mixed Number Series
Mixed number series is an arrangement of numbers in a certain order. This type of series are more than are different order
which arranged in alternatively in single series or created according to any non conventional rule.
EXAMPLE 6, ?, 33, 69, 141, 285
Sol. × 2 + 3, × 2 + 3, × 2 + 3, × 2 + 3,
× 2 + 3, × 2 + 3
4. Geometric Number series
Geometric Number series is an arrangement of numbers in a certain order, where some numbers are this type of series are based on ascending or descending order of numbers and each continues number is obtain by multiplication or division of the previous number with a static number.
In geometric series number is a
combination of number arranged.
EXAMPLE 21, 84, 336, ?, 5376
Sol.
- 21 × 4 = 84
- 84 × 4 = 336
- 336 × 4 = 1344
- 1344 × 4 = 5376
5. Prime Series
When numbers are a series of prime numbers.
EXAMPLE 2, 3, 5, 7, 11, 13, ?
Sol. Here, the terms of the series are prime numbers in order. The prime number, after 13 is 17. So, the answer to this question is 17.
6. Alternate Primes
It can be explained by below example.
EXAMPLE 2, 11, 17, 13, __, 41
Sol. Here, the series is framed by taking the alternative prime numbers. After 23, the prime numbers are 29 and 31. So, the answer is 31.
7. The difference of any term from its, succeeding term is constant(either increasing series or decreasing series)
EXAMPLE 4, 7, 10, 13, 16, 19, __, 25
Sol. Here, the differnce of any term
from its succeding term is 3.
7 – 4 = 3
10 – 7 = 3
So, the answer is 19 + 3 = 22
8. The difference between any two consecutive terms will be either increasing or decreasing by a constant number:
EXAMPLE 2, 10, 26, 50, 82, __
Sol. Here, the difference between two
consecutive terms are
10 – 2 = 8
26 – 10 = 16
50 – 26 = 24
82 – 50 = 32
Here, the difference is increased by 8 (or you can say the multiples of 8). So the next difference will be 40 (32 + 8).
So, the answer is 82 + 40 = 122
9. The difference between any two numbers can be multiplied by a constant number:
EXAMPLE 15, 16, 19, 28, 55, __
Sol. Here, the differences between two
numbers are
16 – 15 = 1
19 – 16 = 3
28 – 19 = 9
55 – 28 = 27
Here, the difference is multiplied
by 3. So, the next difference will be 81.
So, the answer is 55 + 81 = 136
10. The difference can be multiplies by a number which will be increasing by a constant number:
EXAMPLE 2, 3, 5, 11, 35, __
Sol. The difference between two
number are
3 – 2 = 1
5 – 3 = 2
11 – 5 = 6
35 – 11 = 24
11. Every third number can be sum of the two preceding numbers
EXAMPLE 3, 5, 8, 13, 21, __
Sol. Here, starting from third number
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
So, the answer is 13 + 21 = 34
12. Every third number can be product of the preceding numbers
EXAMPLE 1, 2, 2, 4, 8, 32. __
Sol. Here, starting from the third number
1 × 2 = 2
2 × 2 = 4
2 × 4 = 8
4 × 8 = 32
So, the answer is 8 × 32 = 256
Remember
· When the difference between the consecutive numbers is same/constant or the number series is in arithmetic progression.
a, a + d, a + 2d, ..., a + ( n – 1) d.
Where 'a' is first term, d is the common difference.
· When any number series is in the form
a, a + (a + 1), a + (a + 1) + (a + 2), ... ,
nth term of the series be
½[n(n+1)]
ALPHABET SERIES
A series that is made by only alphabetic letters.
EXAMPLE G, H, J, M, ?
Sol.
G H J M Q
+1 +2 +3 +4
ALPHA NUMERIC SERIES
These kind of problems used both mathematical operation and position of letters in the alphabet in forward, backward order.
EXAMPLE K 1, M 3, P 5,
Sol. Alphabets follow the seque
+2 +3 +4 +5
K M P T
And numbers are increasing by 2.
MIXED SERIES
EXAMPLE Z, L, X, J, V, H, T, F, __, __
Sol. The given sequence consists of
two series
(i) Z, X, V, T, __
(ii) L, J, H, F, __.
Both consisting of alternate letters in the reverse order.
Next term of (i) series = R, and
Next term of (ii) series = D
CONTINUOUS PATTERN SERIES
It is a series of small/capital letters that follow a certain pattern like repetition of letters.
EXAMPLE b a a b – a b a – b b a – –
Sol. b a a b b a / b a a b b a / b a
