What is the value of (81 + 82 + 83 + ……… +130)?

Expression : (81 + 82 + 83 + ……… +130)

This is an arithmetic progression with first term, $$a = 81$$ , last term, $$l = 130$$ and common difference, $$d = 1$$

Let number of terms = $$n$$

Last term in an A.P. = $$a + (n - 1)d = 130$$

=> $$81 + (n - 1)(1) = 130$$

=> $$n - 1 = 130 - 81 = 49$$

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

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

= $$\frac{50}{2} (81 + 130)$$

= $$25 \times 211 = 5275$$