Find (61 + 62 + 63 + ……… +110) = ?

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. = $$a + (n - 1)d = 110$$

=> $$61 + (n - 1)(1) = 110$$

=> $$n - 1 = 110 - 61 = 49$$

=> $$n = 49 + 1 = 50$$

$$\therefore$$ Sum of A.P. = $$\frac{n}{2} (a + l)$$

= $$\frac{50}{2} (61 + 110)$$

= $$25 \times 171 = 4275$$

=> Ans - (A)