Question

find the sum of all natural numbers less
than 300 which are divisible by 5.​

Answer 1

Answer:

The numbers into consideration are from 101 to 299 as stated by the question.

So, the first number in the range that is divisible by five is 105, and the last one is 295.

Notice that it is an arithmetic progression, The sum is some thing like this :

S = 105 + 110 + 115 +…..+ 290 + 295

Notice that the common difference is 5.

The number of terms in this series is equal to the index number of the last term in our series.

---> l = a + (n−1) d

---> 295 = 105 + 5 (n−1)

--> (n−1) = (295−105)/5

--> (n−1) = 190/5

--> n = 38+1

--> n = 39

So, the sum of the series will be :

S = n [a+l]/2

S = 39[ 105+295 ]/2

S = 39.400/2

S=39.200

S = 7800

Thus, the answer is 7400

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