What is the common difference of four terms in an A.P.?

In arithmetic progression, the common difference is indicated by d. It’s the distinction between the next term and the one preceding it. It is always constant or the same in arithmetic progression. In other words, if the common difference in a given sequence is constant, we may conclude that this is A.P. or the sequence is as follows: a₁, a₂, a₃, a₄, and so on. In other words, d represents the common difference in the arithmetic progression. The difference between the succeeding and preceding terms. For arithmetic progression, the common difference is always constant or the same.

To find common difference (d) = (a_n + 1 – a_n) or d = (a_n – a_n – 1)

If the common difference is positive, then AP will increase . For Example 4, 8, 12, 16 , 20 , 24 ….. in this series, The difference is positive therefore , AP increases .

If the common difference is negative then AP will decrease. For Example -4, -6, -8 , -10 , -12……., here difference is negative therefore, AP decreases.

If the common difference is zero then AP will be constant. For Example 1, 1, 1, 1, 1,1,1……, here AP will be  constant.

The sequence of Arithmetic Progression will be like a₁, a₂, a₃, a₄, a₅ ……

Common difference (d) = a₂ – a₁ = d  

or, a₃ – a₂ = d

or, a₄ – a₃ = d

or, a₅ – a₄ = d and so on.

Suppose if the four terms are, a₁ = a, a₂ = a + d, a₃ = a + 2d and a₄ = a + 3d ….

Now as per the formula to find common difference =

common difference = a₄ – a₃

= a + 3d – (a+2d)

= a + 3d – a – 2d

= d

Also, common difference = a₃ – a₂

= a + 2d – (a + d)

= a + 2d – a – d

= d

Arithmetic has most likely the longest history at the time. It is a method of computation that has been used since ancient times to derive definite values for routine calculations such as measurements, labelling, and other day-to-day calculations. The phrase derives from the Greek word “arithmos,” which translates as “numbers.”

Arithmetic is the basic branch of mathematics that studies numbers and the characteristics of classical operations such as addition, subtraction, multiplication, and division.

Besides the basic operations of addition, subtraction, multiplication, and division, arithmetic also includes advanced computations such as percentage, logarithm, exponentiation, and square roots, among others. Arithmetic is the study of numerals and their traditional operations.