Question

find the sum of all natural numbers between 50 to 100


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Answer 1

Answer:

Answer is 3775.......

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Answer 2

SOLUTION

The sum of all natural numbers between 50 to 100

EVALUATION

The natural numbers between 50 to 100 are 51 , 52 , 53 , 54 , . . . . , 98 , 99

This is an arithmetic progression

First term = a = 51

Common Difference = d = 52 - 51 = 1

Let 99 is the nth term

Then by the given condition

a + ( n - 1 ) d = 99

⇒ 51 + n - 1 = 99

⇒ 50 + n = 99

⇒ n = 49

Number of terms = 49

Hence the required sum

$\displaystyle \sf{ = \frac{n}{2} \bigg[ 2a + (n - 1)d\bigg] }$

$\displaystyle \sf{ = \frac{49}{2} \bigg[ (2 \times 51) + (49- 1)\bigg] }$

$\displaystyle \sf{ = \frac{49}{2} \bigg[ 102 + 48\bigg] }$

$\displaystyle \sf{ = \frac{49}{2} \bigg[ 150\bigg] }$

$\displaystyle \sf{ = 49 \times 75}$

= 3675

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