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Q:- Find the Sum of the First 100 Natural Numbers.
Answer:- Natural numbers are a set of first 100 numbers from 1 to 100 wherein 1 is the first natural number, and 100 is the last natural number. Natural numbers are part of the natural number system, which includes positive integers from 1 to infinity. These natural numbers are called counting numbers as they do not include zero and negative numbers. The set of natural numbers is a category under a greater set of real numbers. They do not include zero, fractions, decimals, and negative numbers.
The sum of natural numbers is used to determine the summation of numbers. For example, 1+2+3+4…..up to n numbers. Hence we use this formula to find the sum of all the natural numbers.
To calculate the first 100 natural, it can be written as
1,2,3,4……100 in an arithmetic progression. The sum of all natural numbers can be calculated by using the formula
S = n/2[2a+(n-1)×d]
Where n is the total number of natural numbers, which is from 1 to 100, d is the difference between the two consecutive numbers, and a is the first number. There are a total of 100 natural numbers, so n= 100
Then a=1, d=1 and n= 100
By placing all the values in the formula the sum of an AP will be
S = n/2[2a+(n-1)×d]
S= 100/2[2+(100-1)×1]
S=50[2+99]
S=5050
