Answer :

Three equations are different but all are correct and are AP in nature.We need to find three different equations for an Arithmetic Progression (AP) using numbers and symbols.

Arithmetic progression (AP) is a sequence of numbers that follow a certain pattern. It has a common difference between consecutive terms. This difference can be represented by a symbol like "d".So, we can write the first term of the AP as "a", then the second term will be "a+d", the third term will be "a+2d", and so on. Here are three different equations for AP:Equation 1:a, a+d, a+2d, a+3d, a+4d, a+5d, ...Equation 2:8, 11, 14, 17, 20, 23, ... (where a=8 and d=3)Equation 3:-10, -8, -6, -4, -2, 0, 2, ... (where a=-10 and d=2)The above mentioned equations satisfy the condition of Arithmetic progression (AP) where each term is obtained by adding the same constant difference "d" to the previous term. These three equations are different but all are correct and are AP in nature.

Arithmetic Progression (AP) is a sequence of numbers that follow a certain pattern. In a series of numbers that are in Arithmetic Progression (AP), each term is obtained by adding the same constant difference "d" to the previous term. The difference between the successive terms in an AP is constant. The nth term of an AP is given by the formula:a + (n - 1)dWhere 'a' is the first term of the AP, 'd' is the common difference and 'n' is the term number we want to find.To write the equation of AP, we first consider the first term 'a' and then we add 'd' to the first term to get the second term. Continuing this process, we can write the nth term of AP as:a + (n-1)dLet's consider an example:Equation 1:a, a+d, a+2d, a+3d, a+4d, a+5d, ...Here 'a' represents the first term of the AP and 'd' is the common difference between the consecutive terms in the AP. This equation is an infinite series. It is clear that every term in this series is obtained by adding the constant difference "d" to the previous term.Equation 2:8, 11, 14, 17, 20, 23, ...Here a=8 and d=3. In this AP, we can see that the difference between consecutive terms is 3. Thus, each term is obtained by adding 3 to the previous term.Equation 3:-10, -8, -6, -4, -2, 0, 2, ...Here a=-10 and d=2. The difference between consecutive terms in this AP is 2. Thus, each term is obtained by adding 2 to the previous term.These three equations are different but all are correct and are AP in nature.

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