Series
Category : 4th Class
Series
Learning Objectives
What is a Number Series?
A number series is a sequence of many elements made of numbers only. Such sequence is formed by putting the numbers one after another from left to right.
Example:
(i) 1 2 3 4 5 
(ii) 6 5 4 3 2 
(iii)\[\left( 1+1 \right)\text{ }\left( 1+2 \right)\text{ }\left( 1+3 \right)\] 
(iv)\[(1+1)\text{ }(1+2)\text{ }(1+3)\] 
Properties of Number Series
(1) A number series can be in forward or reverse order.
(2) A number series can be in random order.
(3) A number series must have more than one element.
(4) A single number series can have more than one series.
Example:
Look at the following:
(i) 1 2 3 4 5 6 7 (Forward order series)
(ii) 7 6 5 4 3 2 1 (Reverse order series)
(iii) 12, 123, 1234
(iv) 1 5 2 6 3 7
Commonly Asked Question
1. Find the next number.
2 3 4 5 6 7 \[\]
(a) 9 (b) 8
(c) 7 (d) 5
(e) None of these
Answer (b) is correct.
Explanation: Option (b) is correct because the series goes as following:
\[2+1=3\]
\[3+1=4\]
\[4+1=5\]
\[5+1=6\]
\[6+1=7\]
\[7+1=\]
Rest of the options is incorrect because of the correctness of option (b).
Note: This problem is based on forward order series.
2. Find the next number.
(a) 6 (b) 7
(c) 8 (d) 10
(e) None of these
Answer (a) is correct.
Explanation:
Let us see:
R
Rest of the options is incorrect because of the correctness of option (a).
3. Find the next number.
(a) 21 (b) 18
(c) 19 (d) 20
(e) None of these
Answer(c) is correct.
Explanation:
R
Rest of the options is incorrect because of the correctness of option (c).
4. Find the missing number in the following series.
6 2 8 1 10 0 \[\]
(a) 12 (b) 11
(c) 3 (d) 5
(e) None of these
Answer (a) is correct.
Explanation:
Let us see:
The pattern: 
Rest of the options is incorrect because of the correctness of option (a).
5. What comes next in the following series?
(a) 6 (b) 8
(c) 12 (d) 13
(e) None of these
Answer (d) is correct.
Explanation:
Let us see:
Rest of the options is incorrect because of the correctness of option (d).
6. Find the missing number in the series given below.
(a) 17 (b) 18
(c) 19 (d) 20
(e) None of these
Answer (b) is correct.
Explanation: Option (b) is correct because the series goes as following:
\[12\text{ }+\text{ }3\text{ }=\text{ }15\]
\[15\text{ }+\text{ }3\text{ }=\]
\[18\text{ }+\text{ }3\text{ }=\text{ }21\]
\[21\text{ }+\text{ }3\text{ }=\text{ }24\]
Rest of the options is incorrect because of the correctness of option (b).
7. What will come in place of the blank space?
(a) 6 (b) 5
(c) 3 (d) 2
(e) None of these
Answer (b) is correct.
Explanation: Option (b) is correct because the series goes as following:
\[1\text{ }+\text{ }4\text{ }=\]
\[5\text{ }+\text{ }4\text{ }=\text{ }9\]
\[9\text{ }+\text{ }4\text{ }=\text{ }13\]
\[13\text{ }+\text{ }4\text{ }=\text{ }17\]
Rest of the options is incorrect because of the correctness of option (b).
8. Find the missing number in the series given below.
(a) 18 (b) 17
(c) 20 (d) 21
(e) None of these
Answer (b) is correct.
Explanation: Option (b) is correct because the series goes as following:
\[25-2\text{ }=\text{ }23\]
\[23-2\text{ }=\text{ }21\]
\[21-2\text{ }=\text{ }19\]
\[19-2\text{ }=\]
\[17-2\text{ }=\text{ }15\]
Rest of the options is incorrect because of the correctness of option (b).
9. What comes next in the given series?
(a) 6 (b) 7
(c) 8 (d) 5
(e) None of these
Answer (b) is correct.
Explanation:
\[21-2\text{ }=\text{ }19\]
\[19-3\text{ }=\text{ }16\]
\[16-4\text{ }=\text{ }12\]
\[12-5\text{ }=\]
Rest of the options is incorrect because of the correctness of option (b).
10. 
(a) 6 (b) 1
(c) 3 (d) 5
(e) None of these
Answer (b) is correct.
Explanation:
\[21\xrightarrow{-2}19\xrightarrow{-3}16\xrightarrow{-4}12\xrightarrow{-5}7\xrightarrow{-6}\]
Rest of the options is incorrect because of the correctness of option (b).
11. 
(a) 4 (b) 2
(c) 1 (d) 3
(e) None of these
Answer (c) is correct.
Explanation:
\[11\xrightarrow{-2}9\xrightarrow{-2}7\xrightarrow{-2}5\xrightarrow{-2}3\xrightarrow{-2}\]
Rest of the options is incorrect because of the correctness of option (c).
12. 
(a) 545 (b) 656
(c) 666 (d) 565
(e) None of these
Answer (d) is correct.
Explanation: Option (d) is correct.
\[121\xrightarrow{+111}232\xrightarrow{+111}343\xrightarrow{+111}454\xrightarrow{+111}\]
Rest of the options is incorrect because of the correctness of option (d).
What is a Letter Series?
A letter series is a sequence of many elements made of letters of English alphabet only. Such sequence is formed by putting the letters one after another from left to right.
Example:
(i) A B C D 
(ii) D C B A 
(iii) AL BL CB DE 
Properties of Letter series
(1) A letter series can be in forward order.
(2) A letter series can be in reverse order.
(3) A letter series can be in random or jumbled order.
Example:
Look at the following:
(i) H I J M P U
(ii) A B E F J K
(4) A single letter series can have more than one series.
Example:
Look at the following:
(i) A E B F C G
Let us see:
Clearly,
1st series: A B C
2nd series: E F G
(ii) M C P B R A S
Let us see: 
1st series: M O P R
2nd series: C B A
Commonly Asked Question
1. Find the missing letter.
(a) L (b) F
(c) H (d) M
(e) None of these
Answer (a) is correct.
Explanation: The given series is made of two series.
Let us see:
Rest of the options is incorrect because of the correctness of option (a).
2. What comes in place of the blank space?
FA, EC, DE, CG, ____
(a) DJ (b) BH
(c) CI (d) BI
(e) None of these
Answer (d) is correct.
Explanation: The given series contains two series.
Let us see:
Rest of the options is incorrect because of the correctness of option (d).
3. Choose the option that will come next in the series given below.
(a) H (b) G
(c) U (d) T
(e) None of these
Answer (b) is correct.
Explanation: Option (b) is correct because the series is a combination of two series.
Let us see:
Rest of the options is incorrect because of the correctness of option (b).
4. What comes in place of the question mark (?)?
(a) PG (b) QF
(c) QH (d) GQ
(e) None of these
Answer (b) is correct.
Explanation:
Let us see:
1st series: L M N O P Q (forward order series)
2nd series: K J I H G F (reverse order series)
Rest of the options is incorrect because of the correctness of option (b).
5. Find the missing term in the series given below.
(a) MV (b) WL
(c) NU (d) WM
(e) None of these
Answer (b) is correct.
Explanation:
Rest of the options is incorrect because of the correctness of option (b).
6. What would fit in the blank space?
(a) YK (b) XY
(c) KZ (d) JZ
(e) None of these
Answer (c) is correct.
Explanation:
(
: Letter repeats two times.)
Rest of the options is incorrect because of the correctness of option (c).
What is a Mixed Series?
A mixed series is a sequence of many elements made of numbers and letters arranged from left to right. In other words we can say that a mixed series is sequence of diverse elements.
Example:
(i) A 1 B 2 C 
(ii) 12 D 11 E 10 F 
Commonly Asked Question
1. Find the next element in the series given below.
C 4 D 5 E 6 F 7 \[\]
(a) G (b) 8
(c) I (d) H
(e) None of these
Answer (a) is correct.
Explanation: Option (a) is correct because in the given series, letters and numbers take place alternately. Every next letter is one letter ahead from the previous letter and every next number/digit gets increased by 1.
Rest of the options is incorrect because of the correctness of option (a).
2. What comes next in the series given below?
16 T 17 U 18 V \[\]
(a) 19 (b) 21
(c) 20 (d) 22
(e) None of these
Answer (a) is correct
Explanation: Option (a) is correct because in this series, numbers and letters take place alternately. Every next number increases by 1 and every next letter is 1 letter ahead form the previous letter.
Rest of the options is incorrect because of the correctness of option (a).
3. What comes in place of the blank space?
(a) L12 (b) M13
(c) L13 (d) M12
(e) None of these
Answer (b) is correct.
Explanation: Option (b) is correct because of the following reason.
1st series (Letter series): E G I K M
Every next letter of this series takes place skipping one letter in forward alphabetical order.
Let us see:
2nd series (Number series): 5 7 9 11 13
Clearly, every next element of this series increases by 2.
Let us see:
\[5\text{ }+\text{ }2\text{ }=\text{ }7\]
\[7\text{ }+\text{ }2\text{ }=\text{ }9\]
\[9\text{ }+\text{ }2\text{ }=\text{ }11\]
\[11\text{ }+\text{ }2\text{ }=\text{ }13\]
Rest of the options is incorrect because of the correctness of option (b).
4. Fill the blank space.
19 C 18 B 17 A ......
(a) 20 (b) 16
(c) Z (d) B
(e) None of these
Answer (b) is correct.
Explanation: Option (b) is correct because the given series is in the reverse order in which numbers and letters take place alternately. Every next number decreases by 1 and every next letter is one letter backward from the previous letter.
Rest of the options is incorrect because of the correctness of option (b).
5. After how many elements does '\[\div \]' come in the following series? (Count from left)
6 D N 8 L 5 7 \[\div \] 4 9
(a) 9 (b) 5
(c) 7 (d) 8
(e) None of these
Answer (c) is correct.
Explanation:
Let us see:
6 D N 8 L 5 7 \[\div \] 4 9
1 2 3 4 5 6 7 8
'\[\div \]' is the 8th element from left. Hence, it comes after 7 elements.
Rest of the options is incorrect because of the correctness of option (c).
6. In the following series, how many elements come before + ? (Count from left)
L 2 5 T 4 + 9 U
(a) 4 (b) 5
(c) 3 (d) 6
(e) None of these
Answer (b) is correct.
Explanation:
Let us see:
L 2 5 T 4 + 9 U
1 2 3 4 5 6 7 8
Clearly, from left '+' is the 6th element. Hence, 5 elements come before '+'.
Rest of the options is incorrect because of the correctness of option (b).
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