June 27, 2022 # Arithmetic Sequence and Its Various Applications

You might have heard about the concept of arithmetic progression. Arithmetic sequence is a synonym for arithmetic progression. Arithmetic sequence or arithmetic progression is an arranged set of numbers where the difference between any two sequential numbers is a constant, which is also known as the common difference. Let us understand the concept of arithmetic sequence with the help of an example so that you do not face any difficulty in understanding it. For example, we have been given an arithmetic sequence of numbers as follows: 5, 9, 13, 17, 21, 25, 29, and 33. Now if we subtract any two successive numbers, we always get a common number as the difference. Example: 9 – 5 = 4, 13 – 9 = 4, 33 – 29 = 4. In this article, we will learn about the concepts of arithmetic sequence and see its applications.

## The Formula for the Arithmetic Sequence

If you notice carefully the example that we discussed above forms a recognizable pattern. Can you identify it? No? Let me help you out. So, the example of the arithmetic sequence that was given is 5, 9, 13, 17, 21, 25, 29, and 33. Now, 5 is the first number of the sequence. The first number is always denoted with the letter ‘a’ in an arithmetic sequence. Also, the common difference is 4. The common difference is denoted with the letter ‘d’ in an arithmetic sequence. Now, if we write the sequence in the form of alphabets, we get, a (5), a + d (9), a + 2d (13), a + 3d (17), and so on. This is a common pattern that will be followed in all the arithmetic sequences. We have various formulas for arithmetic sequences which are as follows:

• To obtain the nth term of an arithmetic sequence, we use = a + (n – 1)d, where  is the nth term that we need to find, a is the first term of the arithmetic sequence and d is a common difference or the constant of the arithmetic sequence.
• To obtain the sum of first n terms of an arithmetic sequence, we use = n/2 { 2a + (n – 1) d, where is the sum of the first n terms, n is the number of terms, a is the first term of the arithmetic sequence and d is the common difference of the arithmetic sequence.

## Various Applications and Presence of Arithmetic Sequence in Real Life

• An arithmetic sequence is used in the arrangement of seats in a stadium or an auditorium.
• Concepts of simple interest apply the concept of arithmetic sequence as well.
• We determine whether a year is a leap year or not with the concept of an arithmetic sequence.
• Every year during our birthdays, we add one more candle to the cake. This follows the arithmetic sequence too.
• It is a very useful concept in the identification of any sequence.

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