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## introduction

In this article we are to going to discuss, **Sequence and Series Shortcut Tricks**, here you will found that what is a sequence, series, and progression and especially what is difference between sequence and progression.

Today, we will discuss about sequence, progression like arithmetic progression, geometric progression, and harmonic progression.

After that we will discuss **Sequence and Series Shortcut Tricks**, MCQ – Test series, and Explanations with the help of shortcut tricks. So let’s Start each concepts one by one.

To know more about the **Sequence and Series Shortcut Tricks**, click on the below link to buy pdf file or eBook of sequence and series shortcut tricks

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**Sequence**

An arrangement of numbers in a specific pattern is known as a sequence, whereas the arrangement of numbers according to some definite rule, is known as progression.

**Note :-** Here each number is known as term.

**For example;**

10, 100, 1000, 10000,……………….. , is a sequence, because it follows a specific pattern.

Whereas 10, 20, 30, 40,……….., is a progression, because it follows a rule that the difference of each term with its preceding term is always a constant number 10.

**Note:-**

It means a progression is always a sequence but a sequence may not be progression.

We have different types of progression like **Arithmetic progression** (A.P) **Geometric Progression** (G.P) and **Harmonic Progression** (H.P) etc.

**Arithmetic Progression**

The progression in which difference between any two consecutive terms is always a constant number is known as Arithmetic Progression or A.P

Here first term is denoted by ‘a ’ and the constant number is known as common difference which is denoted by ‘d ’.

**For example;** 2, 4, 6, 8,………, 20. Is an infinite A.P

Here a = 2 and d = 2

If you want to know more about A.P and its nth term, its sum of n terms and its properties click on the link below to buy eBook **Sequence and Series Shortcut Tricks**,

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**Geometric Progression (G.P)**

The progression in which ratio between any two consecutive terms is always a constant number is known as Geometric Progression or G.P

Here the first term is denoted by ‘a ’ and the constant number is known as a common ratio which is denoted by ‘r ’.

**For example; **2, 4, 8, 16,………., is an infinite G.P

Here a = 2 and r = 2

To learn more about G.P and its nth term, its sum of n terms and its properties click on the link below to buy eBook **Sequence and Series Shortcut Tricks**,

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**Harmonic Progression (H.P)**

Harmonic Progression is a progression in which reciprocal of its terms are in A.P.

**For Example;**

1/2 ,1/4 ,1/6 , ………. are in H.P because 2, 4, 6,…. are in A.P.

To understand more about H.P and its nth term, its sum of n terms and its properties click on the link below to buy eBook **Sequence and Series Shortcut Tricks**,

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## Shortcut Tricks

In our eBook **Sequence and Series Shortcut Tricks**, we have lots of Shortcut tricks, here we are giving a review of one of them

To find the no. of terms between given two numbers

We will discuss this trick with the help of an example.

Let’s take an example ; find the no. of terms between 337 and 567 which are divisible by 5

Shortcut trick → 337 = 5 x 67 + 2 here q = 67 and r = 2

Also 567 = 5 x 113 + 2 here q = 113 and r = 2

Now required n = 113 – 67 = 64

If you want to know more Shortcut Tricks about Sequence and series Click on the link below to buy eBook **Sequence and Series Shortcut Tricks**,

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## MCQ – Test Series

Q. If the ratio of the sum of n terms of two A.P’s is (5n + 7) : (7n + 9), then the ratio of their 13th terms is given by

- 35/47
- 33/46
- 25/27
- None of these

If you want to get MCQ – Test series with lots of practice questions then Click on the link below to buy eBook **Sequence and Series Shortcut Tricks**,

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## Explanations

**Solution.** 33/46

The solution of this question is done by a shortcut trick which is very quick and give us a fast result.

To check Explanation Click on the link below

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## Conclusion

Thus we observed that sequence and series are very important for our competitive examinations, and hence to learn about its shortcut , we have to buy eBook of **Sequence and Series Shortcut Tricks**,

And to buy **Sequence and Series Shortcut Tricks** click on the link below

http://on-app.in/app/home?orgCode=millu

Thank you

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