Series

**Category : **5th Class

** Series**

**Learning Objectives**

- Number Series
- Letter Series
- Mixed Series

**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 \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\mathbf{1}\,\,\mathbf{2}\,\,\mathbf{3}\,\,\mathbf{4}\,\,\mathbf{5}} \right]\]

(ii) 6 5 4 3 2 \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\mathbf{6}\,\,\mathbf{5}\,\,\mathbf{4}\,\,\mathbf{3}\,\,\mathbf{2}} \right]\]

(iii) 1 3 5 7 \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\mathbf{1}\,\,\mathbf{3}\,\,\mathbf{5}\,\,\mathbf{7}} \right]\]

(iv)\[\left( 1+1 \right)\text{ }\left( 1+2 \right)\text{ }\left( 1+3 \right)\] \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\left( \mathbf{1}\,\,\mathbf{+}\,\,\mathbf{1} \right)\mathbf{ }\left( \mathbf{1 + 2} \right)\mathbf{ }\left( \mathbf{1 + 3} \right)} \right]\]

(v) \[\left( 1\times 1 \right)\,\,\left( 1\times 2 \right)\,\,\left( 1\times 3 \right)\] \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\left( \mathbf{1}\,\,\mathbf{\times }\,\,\mathbf{1} \right)\,\,\left( \mathbf{1}\,\,\mathbf{\times }\,\,\mathbf{2} \right)\,\,\left( \mathbf{1}\,\,\mathbf{\times }\,\,\mathbf{3} \right)} \right]\]

(vi) \[\left( 1\,\,\div \,\,1 \right)\,\,\left( 1\,\,\div \,\,2 \right)\,\,\left( 1\,\,\,\div \,\,3 \right)\] \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\left( \mathbf{1}\,\,\mathbf{\div }\,\,\mathbf{1} \right)\,\,\left( \mathbf{1}\,\,\mathbf{\div }\,\,\mathbf{2} \right)\,\,\left( \mathbf{1}\,\,\,\mathbf{\div }\,\,\mathbf{3} \right)} \right]\]

(vii) (4 - 1) (4 - 2) (4 - 3) \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\left( \mathbf{4 - 1} \right)\mathbf{ }\left( \mathbf{4 2} \right)\mathbf{ }\left( \mathbf{4 3} \right)} \right]\]

**Note:**

**An element is a single member (identity) of a series.** For example, in a number series 1, 2 15 8 12', each 1, 2, 15, 8 and 12 is an element.

**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) Numbers can be repeated in a number series.*

*(5) A single number series can have more than one series.*

*(6) A number series may have some arithmetical signs also.*

**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)

**Commonly Asked Question**

**Find the next number.**

**4 5 6.................**

(a) 7 (b) 8

(c) 3 (d) 2

(e) None of these

**Answer: (a)**

** **

**Explanation:** Option (a) is correct because the series goes as following:

\[4+1=5\]

\[5+1=~6\]

\[6+1=7\]

Rest of the options is incorrect because of the correctness of option (a).

**Note:** This problem is based on forward order series.

**After how many numbers does 2 come in the series given below? (Count from left)**

**1 5 8 2 0 3 **

(a) 5 (b) 2

(c) 1 (d) 3

(e) None of these

**Answer: (d)**

** Explanation:** Option (d) is correct,

**Let us see:**

As 2 is the 4th number from left, it comes after the 3 numbers 1, 5 and 8.

Rest of the options is incorrect because of the correctness of option (d).

3. **Which of the following is not a number series?**

(a) 4 5 (b) 9

(c) 1 2 3 (d) 3 4 5 6

(e) None of these

**Answer: (b)**

** **

**Explanation:** Option (b) is correct because it has a single element 9, but a series is made of more than one element.

Option (a) is incorrect because it has 2 elements.

Option (c) is incorrect because it has 3 elements.

Option (d) is incorrect because it has 4 elements.

Option (e) is incorrect because of the correctness of option (b).

4. **Find the missing number in the following series.**

**8 2 9 1 10 0..........**

(a) 12 (b) 11

(c) 3 (d) 5

(e) None of these

**Answer: (b)**

** **

**Explanation:** Option (b) is correct.

**Let us see:**

Rest of the options is incorrect because of the correctness of option (b).

5. **What comes next in the following series?**

**9 4 8 6 7 8..........**

(a) 6 (b) 9

(c) 5 (d) 4

(e) None of these

**Answer: (a)**

** **

**Explanation:** Option (a) is correct.

**Let us see:**

Rest of the options is incorrect because of the correctness of option (a).

6. **Find the next number in the following series.**

**0, 2, 4, 6..................**

(a) 8 (b) 3

(c) 5 (d) 7

(e) None of these

**Answer: (a)**

**Explanation:** Option (a) is correct because the series goes as following;

\[0+2=2\]

\[2+2=4\]

\[4+2=6\]

\[6+2=8\]

Rest of the options is incorrect because of the correctness of option (a).

7. **What will come in place of the blank space?**

**4-6 7 8**

(a) 1 (b) 5

(c) 3 (d) 2

(e) None of these

**Answer: (b)**

** **

**Explanation:** Option (b) is correct because the series goes as following:

\[4+1=5\]

\[5+1=6\]

\[6+1=7\]

\[7+1=8\]

Rest of the options is incorrect because of the correctness of option (b)

8. **Find the missing number in the series given below.**

**9 6 3 -**

(a) 8 (b) 2

(c) 7 (d) 0

(e) None of these

**Answer: (d)**

** **

**Explanation:** Option (d) is correct because the series goes as following:

\[9-3=6\]

\[6-3=3\]

\[3-3=0\]

Rest of the options is incorrect because of the correctness of option (d).

9. **What comes next in the given series?**

**8 7 6 -**

(a) 4 (b) 3

(c) 5 (d) 1

(e) None of these

**Answer: (c)**

** **

**Explanation:** Option (c) is correct because the series goes as following:

\[8-1=7\]

\[7-1=6\]

\[6-1=5\]

Rest of the options is incorrect because of the correctness of option (c).

**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 \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\mathbf{A B C D}} \right]\]

(ii) D C B A \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\mathbf{D C B A}} \right]\]

(iii) AL BL CB DE \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\mathbf{AL BL CB DE}} \right]\]

** Note**:

**An element of a series is a single member (identity) of that particular series.** For example, in a letter series 'A B C D', each A, B, C and D is a single element. Point to be noted that an element can be made of more than one letter. In a series of 'AB LE BE', each AB, LE and BE is a single element.

**Properties of Letter series**

(1) A letter series can be in forward order.

**Example**

Look at the following:

(i) A B C D

(ii) B C D E

(2) A letter series can be in reverse order.

**Example**

Look at the following:

(i) C B A

(ii) D C B A

(3) A letter series can be in random or jumbled order.

**Example**

Look at the following:

(i) X P Q R A

(ii) B N G I H M

(4) A letter series must have more than one element.

**Example**

Look at the following:

(i) A B

(ii) B C A

(iii) A B C D E

(iv) E F G H

(5) Letters can be repeated in a letter series.

**Example**

Look at the following:

(i) A B C C D A

(ii) B B B A C M N M

(6) A single letter series can have more than one series.

**Example**

Look at the following:

(i) A N B 0 C P

**Let us see:**

Clearly,

1st series: A B C

2nd series: N 0 P

(ii) D P B C Q C B R D A S

**Let us see:**

1st series: D C B A

2nd series: P Q R S

3rd series: B C D

**Commonly Asked Question**

**Find the missing letter.**

**D P C Q…… R A**

(a) B (b) A

(d) E (d) E

(e) None of these

**Answer: (a)**

** **

**Explanation:** Option (a) is correct. The given series is made of two series.

**Let us see:**

Rest of the option is Incorrect because of the correctness of option (a).

2. **What comes in place of the blank space?**

**C N D M E L......**

(a) G (b) H

(c) O (d) F

(e) None of these

**Answer: (d)**

**Explanation: **Option (d) is correct. 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.**

**P J Q I R H………..**

(a) T (b) S

(c) U (d) V

(e) None of these

**Answer: (b)**

** **

**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 (?)?**

**T C V B X A?**

(a) Y (b) N

(c) Z (d) W

(e) None of these

**Answer: (c)**

** **

**Explanation:** Option (c) is correct.

**Let us see:**

**2nd series:** C B A (A reverse order series)

Rest of the options is incorrect because of the correctness of option (c).

5. **Find the missing letter in the series given below.**

**CT M- OT ET**

(a) A (b) C

(c) T (d) M

(e) None of these

**Answer: (c)**

** **

**Explanation:** Option (c) is correct because the last letter in every element of the series is T.

Rest of the options is incorrect because of the correctness of option (c).

6. **What can be fit in the blank space?**

**ADB LDM....... XDH**

(a) ABD (b) NDC

(c) PQR (d) EGZ

(e) None of these

**Answer: (b)**

**Explanation:** Option (b) correct because each element of the given series had D as its middle letter.

Rest of the options is incorrect because of the correctness of option (b).

**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 some cases some symbols may take place in such series. The symbols may be '+', ‘-', ‘\[\times \]’, ‘\[\div \]’?. '>’, '<’, = etc. In other words we can say that a mixed series is sequence of diverse elements.

**Example**

(i) A 1 B 2 C \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\mathbf{A 1 B 2 C}} \right]\]

(ii) 12 D 11 E 10 F \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\mathbf{12 D 11 E 10 F}} \right]\]

(iii) X 4 4 D 5 A + \[\left[ \xrightarrow[\mathbf{Left}\,\,\mathbf{to}\,\,\mathbf{Right}]{\mathbf{X 4 4 D 5 A +}} \right]\]

**Note: Remember from previous chapters (Number Series and Letter Series): An element is a single member of a series.**

**Properties of Mixed Series**

(1) A mixed series can be in forward order.

**Example**

Look at the following:

(i) A 1 B 2 C 3

(ii) L 15 M 16 N 17

(2) A mixed series can be in reverse or backward order.

**Example**

Look at the following:

(i) 5 R 4 Q 3 P 2

(ii) 3 D 2 C 1 B

(3) A mixed series can be in random or jumbled order.

**Example**

Look at the following:

(i) X 2 4 P A

(ii) 2 T Q ? +

(4) A mixed series must have more than one element.

**Example**

Look at the following:

(i) 12 AB

(ii) T 2 Q ? -

(iii) S ? X + 2

(iv) X+ AL 12

(5) Elements can be repeated in a mixed series.

**Example**

Look at the following:

(i) A A 5 2 2 5 C Q ? ?

(ii) T P 9 8 8 9 \[\div \] L \[\div \]

(6) A single mixed series can have more than one series.

**Example**

Look at the following:

(i) P 5 R 7 T 9.

**Let us see:**

**Clearly,**

**1st series (Letter series): P R T**

**2nd series (Number series): 5 7 9**

(ii) 9 N 8 C 7 0 6 B 5 P 4 A 3

**Let us see:**

**1st series (Number series): **9 8 7 6 5 4 3

**2nd series (Letter series): **N 0 P

**3rd series (Letter series): ** C B A

**Commonly Asked Question**

**Find the next element in the series given below.**

**P 2 Q 3 R 4.......**

(a) S (b) C

(c) D (d) M

(e) None of these

**Answer: (a)**

** **

**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)

**What comes next in the following series?**

**9 W 8 V 7 U.......**

(a) X (b) 5

(c) S (d) 6

(e) None of these

**Answer: (d)**

** **

**Explanation:** Option (d) is correct because in the given series, numbers/digits 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 (d).

**What comes in place of the blank space?**

**M 9 P 11 S 13......**

(a) B (b) V

(c) L (d) T

(e) None of these

**Answer: (b)**

**Explanation:** Option (b) is correct because of the following reason.

**1st series (Letter series):** M P S V

Every next letter of this series takes place skipping two letters in forward alphabetical order.

**Let us see:**

**2nd series (Number series): ** 9 11 13

Clearly, every next element of this series increases by 2.

**Let us see:**

\[9+2=11\]

\[11+2=13\].

Rest of the options is incorrect because of the correctness of option (b).

4. **What comes next in the following series?**

**H 3 I 4 K 6 1 M 9 R.......**

(a) 13 (b) 12

(c) 10 (d) 11

(e) None of these

**Answer: (a)**

** **

**Explanation:** Option (a) is correct.

**Let us see:**

1st series (Letter series):

Clearly, every next letter in the given series takes place skipping 0, 1, 2 and 3 letters respectively.

**2nd series (Number series): ** 3 4 6 9 13

**Series Pattern: ** \[3+1=4\]

\[4+2=6\]

\[6+3=9\]

\[9+4=13\]

Rest of the options is incorrect because of the correctness of option (a).

5. **Find the missing element.**

**- L 6 H 3 E 1 C O B**

(a) 10 (b) M

(c) 13 (d) 8

(e) None of these

**Answer: (a)**

** **

**Explanation:** Option (a) is correct.

**Let us see:**

**1st series (Number series): ** 10 6 3 1 0

**Series Pattern:** \[10-4=6\]

\[6-3=3\]

\[3-2=1\]

\[1-1=0\]

Clearly, every next number decreases by 4, 3, 2 and 1 respectively.

**2nd series (Letter series):** L H E C B

**Series Pattern:**

Clearly, every next letter takes place skipping 3, 2, 1 and 0 (Zero) letters respectively in reverse order.

Rest of the options is incorrect because of the correctness of option (a).

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