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Sequences and series (as the name suggests) consists of questions where you are supposed to understand the logic behind a given sequence or series of number/alphabets. Based on this understanding you are supposed to determine either:

- A continuation to the series
- The immediate next term of the series or
- A missing term/terms within the series.

While preparing yourself to solve such questions, you should improve your ability to spot a particular relationship between terms within the series. The common logical premises used for questions are given here.

**Introduction**

Number series is a form of 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.

**Sequence** is the list of numbers written in the specific order.

**For ex.** 1, 4, 9, 16, 25, 36……..

**Some Common types and Their Tricks**

**Type 1 - Addition / Subtraction or Multiplication / Division****Example 1: 19, 23, 39, 75, _, 239**

Most common trick to solve a number series is to solve by checking difference between two adjacent numbers, but difference could not only lead to addition/subtraction but it can also be with multiplication/division.

Therefore, to check whether to think addition wise or multiplication wise in increasing sequence one must make assumption with the help of difference between first and last number of the given sequence.

- If the difference seems to be less according to the number of steps used to make last number from first than we should check addition
- If the difference seems to be large or too large one must check multiplication trick between the adjacent numbers

**In the Exercise 1.** given above, difference between first no. (19) and last number (239) is 220.

Now a question will arise how we will assume whether the difference is more or less. We will assume it by keeping in mind number of steps required to start from first number till last number.**In Example 1**, 19 becomes 239 in five steps, because there are four more numbers between them, one of which we have to find out.

Difference of 220 between 19 and 239 in five steps logically giving priority to addition over multiplication in an increasing sequence like this.

75 + 64 = 139, 139 + 100 = 239 139 is correct answer.

Try yourself:Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?

View Solution

As we can see in above ex. Difference between first number (10) and last number (2609) is 2599 in five steps, which indicate us to check multiplication trick between the numbers.

(288*3) + 4 = 868, is the correct answer.

So, missing term is 169 = 120 + 72

(a) 142

(b) 124

(c) 136

(d) 163

(e) None of these

So, missing term is 82 + 42 = 124

Try yourself:Look carefully for the pattern, and then choose which pair of numbers comes next - 8,11, 21, 15, 18, 21, 22

View Solution

(a) 62

(b) 35

(c) 18

(d) 8

(e) None of these

So, 264 is wrong and must be replaced by 35 + (5

(a) 2147

(b) 729

(c) 125

(d) 1

(e) None of these

Ans.

(a) 5531

(b) 5425

(c) 4621

(d) 5135

(e) 5506

Ans.

-72, -92, -112, -132, -152, -172…

(a) 7

(b) 26

(c) 69

(d) 37

(e) 9

Ans.

(a) 3

(b) 36

(c) 4632

(d) 760

(e) 152

Ans.

Solution: The number should be 770 in place of 760.

×1 +2, ×2 +4, ×3 +6, ×4 + 8, ×5 +10, ×6 + 12, …

(a) 4

(b) 9

(c) 34

(d) 435

(e) 219

Ans.

Solution: The series is 02+ 4, 12 + 2, 32 + 0, 62 - 2, 102 - 4, 152 - 6, 212 – 8…

Hence, 435 should be replaced with 433

(a) 1

(b) 2

(c) 6

(d) 157.5

(e) 45

**Question: 4, 18, 48, 100, 180, ___.**

In case if Type-1 is not applicable in a sequence, then in the next step we must compare given numbers or their differences to square or cube of natural numbers, as in the above example.

Therefore, (7)3-(7)2 = 294, is the correct answer.

1. Perfect Square Series: This Types of Series are based on square of a number which is in same order and one square number is missing in that given series.

Try yourself:In the following options, a few number series are present. One of them has an error, pick the wrong one out:

View Solution

Try yourself:In the sequence given below, a term is missing. The missing term is written in the options that are present below. Find the missing term and choose it from the options below: 8, 12, 21, 37, __

View Solution

(Each cube digit added with seven to become next cube number)**Example 2:**** 729, 6859, 24389, ?, 117649, 205379****Ans.**** **93, 193, 293, 393, 493, 593**Example 3:**** 1000, 8000, 27000, 64000, ?****Ans.**** **103, 203, 303, 403, 503

Try yourself:In the following series, a number is such that it does not belong to the arrangement.

8000, 27000, 64000, 105000

Select the option that has this number:

View Solution

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