The sum of all natural numbers between 100 and 200, which

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The sum of all natural numbers between 100 and 200, which are multiples of 3 is :

1. 5000
2. 4950
3. 4980
4. 4900

Correct Option: B

Numbers divisible by 3 and lying between 100 and 200 are : 102, 105, 108, 111,...................... 198
Let number of terms = n
As we know the formula
a_n = a + ( n – 1 )d
where a_n = Nth Term a = First term , n = Number of terms and d = Common Difference
∴ 198 = 102 + ( n – 1 ) 3

⇒ n − 1 =	198 − 102	= 32
	3

⇒ n = 33

∴ S_n =	Number of terms	= ( First term + Last term )
	2

∴ S_n =	n	= ( a + l )
	2

∴ S_n =	32	(102 + 198) = 4950
	2