2,4,6,8,10,12, …

Look at these numbers. Did you notice the numbers follow a particular sequence?

If you subtract any two consecutive numbers from the list, you will get a difference of 2.

4 – 2 = 2 6 – 4 = 2 8 – 6 = 2 10 – 8 = 2 12 – 10 = 2

An arithmetic sequence is any set of numbers or integers wherein the difference between any two consecutive numbers remains constant. Hence, we can conclude that the above numbers form an arithmetic sequence.

While you’ll learn this mathematical concept in school through various problems and evaluations related to number sequencing, it is always nice to know how these concepts find their relevance in real life. You will be surprised to know that there are numerous examples around us that we simply don’t notice while we are busy with our mundane tasks. So are you ready to explore some real-life examples that make a beautiful arithmetic sequence? Let’s begin!

**12 Real-life arithmetic sequences you probably didn’t know about**

**1. Birthdays**

Birthdays are on the same date every year, and with each passing year, you get a year older, not more, not less. This means your birthdays are in an arithmetic sequence because you will get the same difference of one year when you subtract your age in two consecutive years. So if you are 17 this year, you were 16 last year and will be 18 the following year.

**2. Bank account deposits**

To build a stash of savings, many people have the habit of depositing a fixed amount of money in their bank account every month. So, if you deposit, say, $1000 every month into your account, your account will always hold $1000 more than the previous month. It will look something like this: $1000 in January, $2000 in February, $3000 in March, and so on. Do you see how the deposits are forming an arithmetic sequence here?

**3. Hands of a clock**

Did you ever observe the hands of a clock? Each one, whether the seconds, minute, or hour hand, follows a rhythm and moves in an arithmetic sequence. Therefore, the distance moved with each passing second, minute, or hour remains the same throughout the period of 24 hours.

**4. Stacking chairs**

Stackable chairs are designed so you can stack them one above the other to save space during storage. These chairs are another great example of an arithmetic sequence. Try stacking a few chairs. You will observe the height of the stack increases or decreases depending on whether you’re adding or removing a chair from the stack. The difference in height will always remain the same when you study it for two consecutive arrangements.

**5. Weeks, years, and leap years**

Another classic example of arithmetic sequences is weeks and years. No matter which year you consider, it will have a difference of one year from its successor and predecessor. Similar is the case with weeks in a month. Each week follows a cycle, and a new week begins only when seven days of the previous week have passed. Moreover, leap years are also in an arithmetic sequence and have a difference of four years when two successive leap years are subtracted from one another.

**6. Arrangement of seats in an auditorium**

Have you ever been to an auditorium to enjoy audio and visual performances? If yes, did you notice the seating arrangement there? Most auditoriums and open amphitheaters have a continental seating arrangement. This means all seats are arranged in a concave shape facing towards the stage in an arithmetic sequence. Starting from the first row, every following row has an “n” number of seats more than the previous row until the last row, which has the maximum seats in the auditorium.

**7. Stairs and elevators**

Are you one of those who don’t mind climbing a few stairs, or are you someone who waits for the elevator even if you just have to go to the first floor? Well, we are not going to discuss your choice here but tell you that even stairs and elevators are in an arithmetic sequence. Here the constants are the height of each stair and the distance traveled by an elevator between two successive floors.

**8. Multiples of a number**

Say the times table of any number, and you can obtain its multiples. For example,

2 x 1 = 2 2 x 2 = 4 2 x 3 = 6 2 x 4 = 8 2 x 5 = 10

Here, 2,4,6,8, and 10 are the multiples of two. Observe carefully, and you will notice that each multiple is two more than the previous multiple and two less than the next multiple, making the entire set of multiples of 2 an arithmetic sequence. This fact is not just limited to 2 but stands good for multiples of any number, no matter how big or small.

**9. Seating arrangement**

In an event, how many people can you accommodate on a square table? Four, right? That’s one on each side. But if you combine two square tables, how many people can now sit together? Six. Similarly, adding another one to the lot will allow eight people to sit together. You see how the number of people who can sit together is increasing by two people with the addition of each square table. I hope you can appreciate the sequence here.

**10. An increasing exercise plan**

You must be aware that people new to exercising or those who are resuming exercising after a long time are advised to go slow initially and gradually increase the amount of exercise they are performing. This is recommended so that the body gets used to the new routine slowly and builds stamina without the risk of injury. So, if a person starts with one set, he can move to 3 sets the next week, 5 sets the third week, and so on. Here, the exercise plan is an arithmetic sequence the person follows to stay active.

**11. Decreasing pill dosage**

Similar to the above example, when the doctor reduces a patient’s medication dosage gradually and systematically, it forms an arithmetic sequence. For instance, the doctor advises the patient to have seven pills in a week, then moves to 6 pills, then five pills, and continues this pattern until the patient is entirely off the meds.

**12. Taxi fare**

The taxi fare is also an example of an arithmetic sequence. Setting the initial fixed rate aside, the fare increases sequentially for every extra mile traveled. So, if the fixed charge of a taxi is $15 for the first mile, and every extra mile adds $3 to the fixed amount, the sequence of charges formed for five extra miles will be $3, $6, $9, $12, and $15, where the difference is $3 between two consecutive fares.

**Final words**

Number sequencing is an essential mathematical concept that is taught to students using various activities and worksheets. An arithmetic sequence is a specific type of number sequence which finds its application in different scenarios. Real-life examples of arithmetic sequences make us realize how math is intricately woven into the world around us. You may not notice it immediately, but a close eye can show you the presence of this interesting mathematical concept in our lives.

By recognizing the patterns in an arithmetic sequence, one can make future predictions, and these predictions can help in a multitude of areas, such as finance, engineering, and more. So, try and seek out new arithmetic sequences in the world around you and see for yourself how this concept applies to your surroundings and everyday lives. You will indeed be left spellbound!