What is the value of (91 + 92 + 93 + ……… +140)?

Expression : (91 + 92 + 93 + ……… +140)

This is an arithmetic progression with first term, $$a = 91$$ , last term, $$l = 140$$ and common difference, $$d = 1$$

Let number of terms = $$n$$

Last term in an A.P. = $$a + (n - 1)d = 140$$

=> $$91 + (n - 1)(1) = 140$$

=> $$n - 1 = 140 - 91 = 49$$

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

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

= $$\frac{50}{2} (91 + 140)$$

= $$25 \times 231 = 5775$$

=> Ans - (A)