![]() ![]() What is the Commonly Used Sum of AP Formula? Here, a = a 1 = the first term, d = the common difference, n = number of terms, a n = n th term, S n = the sum of the first n terms. The sum of n terms of an AP can be found using one of the following formulas: must be taken to give a sum of 636?įAQs on Sum of n Terms of an AP What is the Sum of n Terms of an AP Formula? The sum of AP of n natural numbers is n(n+1)/2.The sum of arithmetic progression whose first term is a and the common difference is d can be calculated using one of the following formulas: S n = n/2 (2a+(n−1)d) and S n = n/2 (a 1+a n).In the same way, the sum of infinite AP is −∞ when d 0 \\ We found the sum of infinite AP to be ∞ when d > 0. Substitute all these values in sum of AP formula: Let us consider an example for the sum of an infinite AP. Let's take a look at the following flowchart to get an idea of the formula that has to be used to find the sum of arithmetic progression according to the information available to us. Thus, the sum of arithmetic progression equations are: The above sum of arithmetic progression equation can be written as: ![]() We know that there are totally n terms in the above AP. We see that the sum of corresponding terms of equation (1) and equation (2) yield the same sum which is 2a+(n−1)d. S n =a + (a+d) + … + (a+(n−2)d) + (a+(n−1)d) → (1)īy reversing the order of the terms of this equation: The sum of n terms of this progression is: Let us consider the arithmetic progression with n terms: In this section, we are going to learn the proof of sum of n terms of an AP formula. ![]()
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