**Arithmetic Progressions**

Introduction

In mathematics, an arithmetic progression (AP) is a sequence of numbers that follow a pattern such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2.

Applications of Arithmetic Progressions

In this section, we shall discuss about the everyday applications related with the arithmetic sequences and arithmetic series.

**Arithmetic Progressions in Daily Life**

You must have observed that in our daily Life, many things follow a certain pattern.Like we all wake up every day and go to school every day but that is not what we are here to discuss.

• Building a ladder with sloping sides -the length of each rung would form an Arithmetic progression.

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Conclusion

We have seen how

Arithmetic Progressions

are used in our ordinary day to day life and we hope that now you all will look at life with a different perspective.

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What is Arithmetic Progression ?

Why Exactly Are We Here?

We are here to discuss the real life applications of the topic that many of you might have studied in your 10th standard and also because we want to win the trophy!

Old Faithful : Yellow Stone National Park

Old faithful is a natural geyser (at the yellow stone national park) that produces long eruptions that are easily predictable and suprisingly no one controls it!

The time between eruptions is based on the length of the previous eruption :

If an eruption lasts one minute, then the next eruption will occur in approximately 46 minutes.

If an eruption lasts for 2 minutes then the next eruption will occur in 58 minutes.

The eruptions thus occur in the sequence of 46, 58, 70, 82, 94..... with a common difference of 12.

Savings Schemes

In saving schemes where you deposit Rs. 1000 and every year get an increment of Rs.50.

Thus forming another A.P : 1000,1050,1100,1150.......

Ladder Building

Potato Race

Ever seen a potato race?Believe it or not there is A.P applied even in a simple race,The distance difference between each potato increases in successful proportions for example:

5m,8m,11m,14m.....

In Movie Halls the first row has 10 seats the second row has 12 seats and so on, an arithmetic progression forms : 10,12,14,16....

Uniform increase in the speed at regular intervals.

Speed of an aircraft, finding the sum of n terms of natural numbers.

increase or decrease in the costs of goods.

fare of taxi,

finding multiples of numbers within a range.

sales and production

are some more uses of Arithmetic Progression.

MORE A.P

Mathematical Formula

If the initial term of an arithmetic progression is a and the common difference of successive members is d, then the nth term of the sequence (a_n) is given by:

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Created by - Manan and Karan