The sum (101 + 102 + 103 + .... + 200) is equal to :

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The sum (101 + 102 + 103 + .... + 200) is equal to :

1. 15000
2. 15025
3. 15050
4. 25000

Correct Option: C

Let S = 101 + 102 + 103 + .... + 200
S = (100 + 1) + (100 + 2) + (100 + 3) + ...+ (100 + 100)
Thus, it consists of 100 terms.
S = (100 + 100 + 100 + .... 100 times) + (1 + 2 + 3 + ...... + 100)
S = (100 × 100) + (1 + 2 + 3 + ..... + 100)
S = (10000) + (1 + 2 + 3 + ... + 100)

S = 10000 +	100 × (100 + 1)
	2

S = 10000 + 5050 = 15050

We can find the required answer with the help of given formula :

Here, a = 101, d = 102 – 101 = 1 , L = 200
∴ L = a_n = a + (n – 1)d
200 = 101 + (n – 1)1
⇒ n – 1 = 99
n = 100

S_n =	n	[a + L]
	2

S_n =	100	[101 + 200]
	2

∴ S_n = 50 × 301 = 15050