Given:
The first 30 natural numbers are 1, 2, 3, 4, ..., 30.
Concept:
The sum of an arithmetic series is the number of terms in the series times the average of the first and last terms.
Formula:
See Also
The sum of 3 consecutive numbers is 33. Find those numbers.Integers - Definition, Rules, Properties and ExamplesThree consecutive even integers have a sum of 30 . Find the integers.The product of two consecutive natural numbers is 30. Find the numbers.Sn = n/2(a + l)
where:
Sn is the sum of the series
n is the number of terms in the series
a is the first term in the series
l is the last term in the series
Solution:
Define the variables:
n = 30 (number of terms)
a = 1 (first term)
l = 30 (last term)
Substitute the values in the formula:
Sn = n/2(a + l) = 30/2(1 + 30) = 30/2 × 31 = 465
Therefore, The sum of the first 30 natural numbers is 465.
![[Solved] Find the sum of first 30 natural numbers. (2024)](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mP8/h8AAvMB+NzmkbcAAAAASUVORK5CYII=)