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Find the sum of the first 100 natural numbers.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The sum of the first 100 natural numbers is 5050. Four main characteristics of natural numbers are divided into groups, and they are as follows:
Closure property – Under addition and multiplication, natural numbers are always closed. A natural number will always result from the addition and multiplication of two or more natural integers. Natural numbers do not adhere to the closure property when it comes to subtraction and division, which implies the outcome of subtracting or dividing two natural numbers might not be a natural number.
Table of content
Commutative Property
- Natural number addition and multiplication demonstrate the commutative characteristic. For example, x + y = y + x and a × b = b × a
- Natural number division and subtraction do not exhibit the commutative characteristic. For example, x – y ≠ y – x and x ÷ y ≠ y ÷ x
Associative property – In the case of addition and multiplication of natural numbers, a + (b + c) = (a + b) + c and a (b c) = a × ( b × c ) = ( a × b ) × c., the associative property stays true. On the other hand, the associative property does not apply to the operations of subtracting and dividing natural numbers.
Distributive property
- Natural number multiplication is always distributive relative to addition. For example, a × (b + c) = ab + ac
- Natural number multiplication also has a distributive advantage over subtraction. For example, a × (b – c) = ab – ac
- Now we have to find the sum of the first 100 natural numbers.
Equation for Computing Total of n Natural Integers
The equation for computing the total of n natural integers: Sn = n/2 (a + an)
Here,
- Sn is the sum of the arithmetic sequence
- d is the common difference between the terms,
- a is the first term
- n is the total number of terms in the sequence
- an is the last term of the sequence.
Here a = 1
an = 100 and n = 100
Substituting the values we get:
Sn = 100/2 (1 + 100)
Sn = 100/2 x 101
Sn = 50 x 101
Sn = 5050
Therefore, the sum of the first 100 natural numbers is 5050.
Summary:
Find the sum of the first 100 natural numbers.
The first 100 natural numbers added together equal 5050. Natural numbers are a part of the number system which includes all the positive integers from 1 to infinity and are also used for counting purposes.
