The sum of the first and 100th terms of an arithmetic series is 101. Find the sum of the first 100 terms.

5050

Step-by-step explanation:

The sum of an arithmetic series is the product of the number of terms and the average value of a term. That average value can be found as the average of the first and last terms. Then for (a1 + a100) = 101, the average term is ...

(a1 + a100) / 2 = 101/2 = 50.5

Since there are 100 terms, the sum of them is ...

100 * 50.5 = 5050

The sum of the first 100 terms is 5050.