Question

Find the sum of all odd natural numbers less than 200.(A) 1000 (B) 10100(C) 9900 (D) 10000

Answer 1

Solution:-
Odd natural numbers less than 200 = 1, 3, 5, 7, 9.......199
Here, a = 1 and common difference = 2
Number of terms = n
And nth term is 199.
So, 
199 = a + (n - 1)d
⇒ 199 = 1 + (n - 1)2
⇒ 199 - 1 = 2n - 2
⇒ 198 + 2 = 2n
⇒ n = 200/2
⇒ n = 100
Now, sum of n number of terms = Sn = n/2{2a +(n - 1)d}
S₁₀₀ = 100/2{2 *1 + (100 -1)2}
= 50{2 + (99*2)}
= 50(2 + 198)
= 50*200
= 10000
So, the sum all odd natural number less than 200 is 10000.
So, the option (D) is correct.