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2067 Supp Q.No. 2a Find the sum of all the natural numbers between 1 and 100 which are divisible by 5. Ans: 1050 ​

User Nikhil Patil
by
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1 Answer

9 votes
9 votes

5

Answer:

1050

Explanation:

Natural Numbers are positive whole numbers. They aren't negative, decimals, fractions. We can just divide 5 into 100 to find how many natural numbers go up to 100 and just add them but that is just to much.

There is a easier method.

E.g: Natural Numbers that are divisible by a Nth Number. is the same as adding the Nth Numbers to a multiple of that Nth Term. For example, let say we need to find numbers divisible by 2. We know that 4 is divisible by 2 because 4/2=2. We can add the Nth numbers which is 2 to 4. 4+2=6. And 6 is divisible by 2 because 6/2=3. We can call this a arithmetic series. A series which has a pattern of adding a common difference

Back to the problem, we can use the sum of arithmetic series formula,


y = x( \frac{z {}^(1) + {z}^(n) }{2} )

Where x is the number of terms in our sequence. Z1 is the fist term of our series. ZN is our last term. And y is the sum of all of the terms

The first term is 5, the numbers of terms being added is 20 because 100/5=20. The last term is 100.


y = 20( (5 + 100)/(2) )


y = 20( (105)/(2) )


y = 1050

User Franz Gleichmann
by
2.5k points
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