Let the nth term and sum of the series upto n terms of the series be Tn and Sn , respectively. Then, ⇒Sn=
1
5
+
3
5
+1+
7
5
+
9
5
+....... Multiplying the above equation by 5, we get ⇒5Sn=1+3+5+7+9+....... up to n terms This is the sum of first odd natural numbers. As we know that, sum of the first n odd natural numbers i.e 1 + 3 + 5 +7 +9 + ...up to n terms = n ⇒ ⇒5Sn=n2⇒Sn=n2∕5 For n=50,S50=502∕5=500. Hence, option 2 is the correct answer.