Therefore, the sum of the even numbers from 1 to 200 is 10,100įAQs on Sum of Even Numbers Formula What is the Meaning of the Sum of Even Numbers Formula? Solution: We know that are 100 even numbers between the numbers 1 to 200. Therefore, the sum of the first 10 multiples of 8 is 440Įxample 3: Determine the sum of even numbers from 1 to 200. Now, let us find the sum of the first 10 multiples of 8 by using the arithmetic progression formula S n=1/2×n where a = 8 and d = 8 Therefore, the sum of the first 20 even numbers is 420Įxample 2: Find the sum of the first 10 multiples of 8 Now, let us find the sum of the first 20 even numbers Solution: The natural numbers present among the first are 20 numbers. Math will no longer be a tough subject, especially when you understand the concepts through visualizations with Cuemath.Įxample Using Sum of Even Numbers FormulaĮxample 1: What is the sum of the first 20 even numbers? Let us look at a table for the sum of even numbers from 1 to 10 that are consecutive: S n = 2+4+6+8+10+. Hence, the sum of even numbers formula = n(n+1) Sum of First Ten Even Numbers 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, for any sequence, the sum of n terms of an AP is given by: S n= (1/2)× n …….(2)Ī = First term of an arithmetic progressionĭ= Common difference in an arithmetic progression Let us derive the sum of even numbers formula by using arithmetic progression. Let the sum of first n even numbers is S n, so S n = 2+4+6+8+10+………………….+(2n) ……. S = n(n+1) , where n is the number of terms in the seriesĭerivation of Sum of Even Numbers Formula This implies 2(sum of n natural numbers) = 2/2 = n(n+1) Sum of Even Numbers Formula We need to obtain the formula for 2 + 4+ 6+ 8+ 10 +. 2n. The sum of even numbers goes on until infinity. The sum of even numbers formula can also be evaluated using the sum of natural numbers formula. The sum of even numbers formula is determined by using the formula to find the arithmetic progression. Let us learn about the formula and solve a few examples in this section. To determine the sum of even numbers formula, we need to use the sum of arithmetic progression formula or the sum of natural numbers formula. As we already know that even numbers are those numbers that are divisible by the number 2, for example, 2,4,6,8,10 and so on. The sum of even numbers is the numbers starting from 2 that goes till infinity.
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