Question

The sum of first 100 natural numbers is​

Answer 1

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$sum = \frac{n}{2} (2a + (n - 1)d) \\ \\ sum = \frac{100}{2} (2 \times 1 + (100 - 1)1) \\ \\ sum = 50 \times 101 \\ \\ sum = 5050$

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Answer 2

TO FIND :- Sum of first 100 natural number.

SOLUTION

Natural Numbers begin from 1 and increasing 1 in sequence like 1,2,3...

This Question can be solved by the concept of ARITHEMATIC PROGRESSION.

Here,

AP = 1,2,3,4.... 100

First Term ( a ) = 1

Common difference ( d ) = 1

Last term ( l ) = 100

Now, first we have to calculate the number of terms first

l = a + (n - 1)d

=> 100 = 1 + ( n - 1) 1

=> 100 = 1 + n - 1

=> n = 100

We can put this value in the below formula to calculating the sum of 100 terms

$s_n = \frac{n}{2} (a + l) \\ \\ \\ \\ = \frac{100}{2} (1 + 100) \\ \\ \\ \\ = 50 \times 101 \\ \\ \\ = \boxed{5050}$

Therefore the sum of first 100 natural numbers is 5050.