The sum of 1 to 10 consecutive even numbers is shown in the table below.įind the first ten even numbers by counting them. Hence, the sum of even numbers formula = n(n+1) Also read about: Great Mathematicians of India. Therefore, if we put the values in equation 2 with respect to equation 1, such as a = 2, d = 2, and suppose last term, l = (2n) (1)īy arithmetic progression (AP), we know that, for any sequence, the sum of n terms of an AP is given by: Sn = (1/2)× n …….(2)Ī = First term of an arithmetic progressionĭ= Common difference in an arithmetic progression Let's use arithmetic progression to arrive at the formula for the sum of even numbers. Derivation of Sum of Even Numbers Formula
#EVEN NUMBERS SERIES#
S = n(n+1), where n is the number of terms in the series Also read about: Father of mathematics. This implies 2(sum of n natural numbers) = 2/2 = n(n+1) Sum of Even Numbers Formula using AP We need to obtain the formula for 2 + 4 + 6 + 8 + 10 +. The formula for the sum of natural numbers can also be used to evaluate the sum of even numbers. Even numbers can be added up indefinitely.
The formula for calculating the arithmetic progression is used to determine the formula for the sum of even numbers. The sum of the arithmetic progression formula or the sum of natural numbers formula must be used to calculate the sum of even numbers. As we already know, even numbers are those that can be divided by 2, such as 2, 4, 6, 8, 10, and so forth. The numbers beginning at 2 and continuing until infinity are the sum of even numbers. Sum of Even Numbers: Derivation and Solved Examples FAQs.Derivation of Sum of Even Numbers Formula.
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