If the 10 t h , term of an A.P. is 1 20 , and its 20 t h , term is 1 10 , then the sum of its first 200 , terms is.

Step-by-step solution

Let, a   &   d is the first term and common difference of arithmetic progression respectively, then T 10 = 1 20 = a + 9 d         . . . i T 20 = 1 10 = a + 19 d         . . . i i After solving i and i i , we get a = 1 200 ,   d = 1 200 Now S 200 = 200 2 2 200 + 199 200 = 201 2 = 100 1 2 .