Before learning the formula for the sum of consecutive numbers, let’s recall what consecutive numbers are. Consecutive numbers are those numbers that differ by 1 which means, the difference between two consecutive numbers is always 1. These numbers are followed by each other in increasing order. For example, 11 and 12 are consecutive numbers, where 12 – 11 = 1, i.e. the difference between 12 and 11 is 1 also, 12 is followed by 11 or 11 is preceded by 12. Thus, consecutive numbers form an arithmetic sequence with a common difference of 1. So, we use the formula of an arithmetic sequence to calculate the sum of consecutive numbers.
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Sum of Consecutive Numbers Formula
As mentioned above, consecutive numbers form the arithmetic sequence. So, let’s consider the consecutive numbers as a, a + d, a + 2d,…., where the common difference d = 1.
In an AP, when the first term and the last term is known, we can find the sum of the sequence using the formula,
Sn = (n/2)[first term + last term]
Here, n is the number of terms in the sequence.
Therefore, the sum of n consecutive numbers is given by the formula:
| Sum of n consecutive numbers = (n/2) (First number + Last number)
n = Last number – First number + 1 |
|---|
Also, check: Sum of Arithmetic sequence Formula
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Examples
Let’s have a look at the examples on the sum of consecutive numbers.
Sum of Consecutive Numbers from 11 to 20
Consecutive numbers from 11 to 20 are: 11, 12, 13,…, 20
Here,
First number = 11
Last number = 20
n = Last number – First number + 1 = 20 – 11 + 1 = 10
Thus, the sum of consecutive numbers from 11 to 20 = (10/2) × (11 + 20) = 5 × 31 = 155
Try out: Consecutive Integers Calculator
Sum of Consecutive Numbers from 1 to 50
Consecutive numbers from 1 to 50 are: 1, 2, 3, 4,…, 50
Here,
First number = 1
Last number = 50
n = Last number – First number + 1 = 50 – 1 + 1 = 50
Thus, the sum of consecutive numbers from 1 to 50 = (50/2) × (1 + 50) = 25 × 51 = 1275
Sum of Consecutive Numbers from 1 to 100
Consecutive numbers from 1 to 100 are: 1, 2, 3, 4,…, 100
Here,
First number = 1
Last number = 100
n = Last number – First number + 1 = 100 – 1 + 1 = 100
Thus, the sum of consecutive numbers from 1 to 100 = (100/2) × (1 + 100) = 50 × 101 = 5050
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