About Formula For Adding Consecutive Numbers
Before learning the formula for adding consecutive numbers, we must first understand what consecutive numbers are. The consecutive numbers are those that appear in ascending sequence after each other. The difference between two successive numbers is always one.
12, 13, 14,..., or -2, -1, 0, 1, 2,.... are examples of consecutive numbers. Every list of consecutive numbers is an arithmetic sequence since the difference between every two consecutive numbers is the same (as 1). As a result, the sum of the arithmetic sequence formula can be used to add successive numbers.
What is the Addition Formula for Consecutive Numbers?
We know that a + (a + d) + (a + 2d) +... + (a + (n-1) d) is the sum of an arithmetic sequence of n terms: (n/2) (first term + last term) = sum of n terms
The difference between any two consecutive numbers is d = 1, as we saw in the previous section.
So [a + (a + 1) + (a + 2) +.... +{a + (n-1)}] is the formula for adding n successive integers.
Sum of n consecutive numbers = (n/2) (first number + last number)
Example: Find the sum: 46 + 47 + 48 + ... + 103 by using the formula for adding consecutive numbers.
Sol: we have to find sum of 46 + 47 + 48 + ... + 103.
Here, the number of numbers is, n = 103 - 46 + 1 = 58.
First number = 46.
Last number = 103.
Using the sum of consecutive numbers formula:
Sum of n consecutive numbers = n2n2 (first number + last number)
Sum of 58 consecutive numbers = 582582 (46 + 103) = 4321
Answer:46 + 47 + 48 + ... + 103 = 4,321.
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