Expression : (61 + 62 + 63 + ……… +110) This is an arithmetic progression with first term, $$a = 61$$ , last term, $$l = 110$$ and common difference, $$d = 1$$ Let number of terms = $$n$$ Last term in an A.P. = $$a + (n - 1)d = 110$$ => $$61 + (n - 1)(1) = 110$$ => $$n - 1 = 110 - 61 = 49$$ => $$n = 49 + 1 = 50$$ $$ herefore$$ Sum of A.P. = $$frac{n}{2} (a + l)$$ = $$frac{50}{2} (61 + 110)$$ = $$25 imes 171 = 4275$$ => Ans - (A)