Series Completion

**Category : **10th Class

**WHAT IS SERIES COMPLETION?**

A series is made up of alphabetical letters or numerals or combination of both. In this chapter the questions are asked in the given two ways:

1. Find one or more missing terms in the given number series or alphabet series or alpha-numeric series.

2. Find a wrong term in the given number series or alphabet series or alpha-numeric series.

**Trick: **

To find out a missing or wrong term, just decipher the pattern in the given series.

**EXAMPLE**

**1. Choose the missing term in the given number series.**

** 165, 195, 255, 285, 345, ?**

(a) 375 (b) 420

(c) 435 (d) 390

**Explanation (a):**

We observe the given series as follows:

Clearly, the required term = 345 + 30 = 375.

**2. Choose the missing term.**

43, ?, 66, 83, 91, 106, 123

(a) 58 (b) 51

(c) 60 (d) 56

**Explanation (b):**

We see that

83 - 66 = 17

91-83=8

106-91 = 15

123- 106= 17

So, the difference between four consecutive terms in pairs is 8, 15, 17; 8, 15, 17.

\[\therefore \]Required term = 43 + 8 = 51.

**3. Identify the wrong number in the series.**

**69, 55, 26, 13, 5**

(a) 55 (b) 5

(c) 26 (d) 13

**Explanation (b):**

Clearly, in the given series, each term is one more than the product of the digits of the preceding term.

Thus, \[\left( 6\times 9 \right)+1=55,\left( 5\times 5 \right)+1=26,\left( 2\times 6 \right)+1=13.\]

So, 5 is wrong number in the series and must be replaced by \[\left( 1\times 3 \right)\]+1 i.e., 4.

Hence, the answer is (b).

**4. Choose the missing term.**

AB, DEF, HUK, ?, STUVWX

(a) MNOPQ (b) LMNOP

(c) LMNO (d) QRSTU

**Explanation (a):**

First letter of each term except the first term is two more than the last letter of the previous term.

1st letter of required term = K + 2 letters = M

So, required term = MNOPQ.

**5. Choose the missing term.**

** 7T19, 9Q16, 11N13, 13K10, 15H7, ? **

(a) 17E4 (b) 18F5

(c) 17E3 (d) 18D4

**Explanation (a):**

Observing the given series, we obtain the required term as follows:

So, the required term is 17E4.

**6. A letter series is given in which some letters are missing. The missing letters are given in the proper sequence as one of the options. **

** Find the correct option.**

**c_ bba_ cab_ ac_ ab_ ac**

(a) abcbc (b) acbcb

(c) babcc (d) bcacb

**Explanation (b): **

The pattern is : cabbac/cabbac/cabbac.

So, the complete series is : cabbaccabbaccabbac.

**7. In the given question, a series of letters and numbers is given, the terms of which follow a certain pattern in groups. **

** However, some terms in the series are missing/ which are given in the same order as one of the alternatives below the series. **

** Choose the correct alternative.**

2 3 B __6 __ F G __ 5D __ 8 H I

(a) W, 8, 7, I, 6 (b) D, 8, 6, C, 7

(c) E, 8/ 7, D, 9 (d) C, 1, 4, E, 9

**Explanation (d):**

From the alternatives, it is clear that the series can be divided into groups of 4 terms each, as shown below:

2 3 B _ / 6 _ FG / _ 5D _ / 8 _ HS

Clearly, the first number in each group represents the position of the letter at the third place in the English alphabet.

And the second number in each group represents the position of the letter at the fourth place in the English alphabet.

Substituting other terms of (d) into the series, we get:

2 3 B C / 6 7 F G / 4 5 D E / 8 9 H I

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