Question

Find the sum of all natural numbers between 100 and 150.​

Answer 1

Answer:

The number series 1, 2, 3, 4, . . . . , 149, 150. Therefore, 11325 is the sum of positive integers upto 150.

Answer 2

The sum of all natural numbers between 100 and 150. is 6375.

• A term which is called common difference is used in the case of arithmetic progressions and sequences. One example of sequence in real life is the commemoration of birthdays of individuals. In this instance, there is typically a one-year gap between consecutive celebrations of the same person.
• The difference between any term and its preceding term is an arithmetic sequence's is referred to as the common difference. An arithmetic sequence always adds (or subtracts) the same amount to go from one term to the next.
• The amount that is added (or removed) at each point in an arithmetic progression is referred to as the "common difference" because, if we subtract (that is, if we determine the difference of) succeeding terms, we will always arrive at this common value.

Here, according to the given information,

We need to find the sum of all natural numbers between 100 and 150, that is, $100+101+...+150.$

Let the first term be 100, the last term is 150 and the common difference is 1 as they are natural numbers.

Also, the number of numbers between 100 and 150 is, 51.

Then, we get,

Sum of 51 terms = $\frac{51(100+150)}{2} = \frac{51.(250)}{2} = 6375.$

Hence, the sum of all natural numbers between 100 and 150. is 6375.

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