Among the choices, find the sum of the first 100 even natural numbers which are divisible by 5.

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50,555

50,500

55,555

55,550

answer is D.

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Detailed Solution

We know that, the first 100 even natural numbers that are completely divisible by 5 are:
10, 20, 30,…
The above numbers are in the form of an AP.
So,

a 1 = a = 10 d = 10 n = 100

The formula that gives the sum of the n terms is,

S n = n 2 [2 a + (n − 1) d]

.
Substitute the known values in the above formula.

S 100 = 1002 [2 (10) + (100 − 1) (10)]

= 50 [20 + 990] = 50, 500

The sum of the first 100 even natural numbers that are divisible by 5 is 50,500.
Hence, option 4) is correct.

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