# Where do we use arithmetic sequence in real life?

One of my priorities as a math teacher is to show real-world math to students wherever and whenever possible. I must admit that it is not always convenient. When I was in college and in the early stages of my teaching career, I was all about learning math. It was not how I could use it in real life.

I’ve set a challenge for myself to find real-life scenarios for every math concept I have learned. I’ve even attempted to capture the situation in reality, but it’s not always easy, particularly because I often have ideas when I am eating or lying in bed.

Recently, I’ve been thinking about arithmetic sequences and their uses in our life. It seems to be easy, doesn’t it? They are sequential. There are several direct cases. But I’d like to see more applications of arithmetic sequence in real life. I still didn’t want the case to be a straight line with always positive figures and positive angles.

I figured out several cases where we use arithmetic sequence in our daily lives. Most of them are the really fun part. But before that, let’s have an idea about what arithmetic sequence actually is?

## What is Arithmetic Sequence?

An arithmetic sequence is a collection of numbers that follow a certain pattern. If you take every number in the sequence and divide it by the previous one, and the answer is either the constant or the same, the sequence is an arithmetic sequence.

For example: 2, 4, 6, 8, 10…

It can be calculated by adding a common difference in the first term. Then you have to keep adding the common difference in the previous term to get the complete sequence.

### Common Difference

The difference between each term is denoted by the letter d. It is the constant difference between all pairs of successive or consecutive numbers in a series. To jump from one term to another, the common difference is used by adding or subtracting it in the previous term.

• If the common difference between successive terms is positive, it means that the sequence is increasing.
• However, if the difference is negative between the terms, it means that the sequence is decreasing.

The common difference in an arithmetic series can be calculated by subtracting the previous term from the current term.

### Nth Term

Nth term is the last term in the sequence that can be accumulated by keep adding the common difference in successive terms until the nth term is reached. The nth term can be calculated using an nth term calculator.

The nth term can be calculated using the below formula.

nth term = a + (n – 1)d

## Where do we use arithmetic sequence in real life? Here are some of the scenarios I’ve imagined where arithmetic sequences are used in our real lives. I will be delighted if you include these scenarios when working with arithmetic sequences for your studies.

### 1. Stacking Up

Stacking crockery (cups, plates), furniture (chairs) on each other is an example of the arithmetic sequence. Anything can be stacked, but the situation changes when two things fit inside one another. Pyramid-like patterns, where items are increasing or decreasing in a continuous way.

If you are a fan of any outdoor sports or movies, you probably have visited a stadium or cinema. Seats in a stadium or a cinema are two examples of the arithmetic sequence being used in real life.

### 2. Arranging and Filling

A situation might be that seats in each line are decreasing by three from the previous line. This is something I used in one of my arithmetic sequence problems. Another good example of an arithmetic sequence is filling something. The bottle can be empty or filled with items. An example could be a hand basin or a water tub is filled. Draining water should also be taken into account as a sequence. The variables would be the rate at which the item is filed against time.

### 3. Seating

Seating is arranged around tables. Consider a restaurant. A square table seats four people. A total of six people may be seated when two square tables are joined together. When three square tables are joined together, eight people may be seated. This is a fantastic cause. You can also put in six chairs if you have a rectangular table.

### 4. Fencing

Examples of perimeters and fencing can be useful here. Consider if installing a fence sheet to either side of a rectangular boundary would affect the perimeter. A lawn could have one sheet on every side or be modified such that it is not square. Each side of the lawn may have two panels. Find the new perimeter each time. Fencing can be done in several ways. Sequences come into play when we try to figure out installing the fence on each or a few sides.

### 5. Natural events

Negative number variations are not as straightforward to detect. Our minds normally go to sea level or temperature. There are few interesting sites in the world that are under sea level. I think it would be nice to include them in this list. During rainfall, the surface of the water began at 220 feet below sea level and rose at a rate of such and such every half an hour.

Situations like underwater diving may also be considered as the application of arithmetic sequence. Did you know that a diver can descend no faster than 66 feet per minute and climb no faster than 30 feet per minute? I’m sure many students don’t understand why, and this might lead to some interesting and responsible discussions.

Wrapping Up

These applications of arithmetic sequence mostly go unnoticed because we don’t realize its existence in our routine work. It’s very good for the brain to build these scenarios. By practicing in this way, students can make sure that their skills are getting polished.

If this post helped you grasp the idea of an arithmetic sequence, you should use some of these explanations and come up with a few more applications on your own.