(91 + 92 + 93 + ……… +110) is equal to

Expression : (91 + 92 + 93 + ……… +110)

This is an arithmetic progression with first term, $$a = 91$$ , last term, $$l = 110$$ and common difference, $$d = 1$$

Let number of terms = $$n$$

Last term in an A.P. = $$a + (n - 1)d = 110$$

=> $$91 + (n - 1)(1) = 110$$

=> $$n - 1 = 110 - 91 = 19$$

=> $$n = 19 + 1 = 20$$

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

= $$\frac{20}{2} (91 + 110)$$

= $$10 \times 201 = 2010$$