This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the series. This is an arithmetic progression with the first term a_1 = 101, the last term a_n = 200, and a common difference d = 1. Step 2: Find the number of terms (n). The formula for the n-th term of an arithmetic progression is a_n = a_1 + (n-1)d. Substitute the known values: 200 = 101 + (n-1) × 1. 200 - 101 = n - 1. 99 = n - 1. n = 99 + 1 = 100. There are 100 terms in the series. Step 3: Calculate the sum of the arithmetic progression. The formula for the sum of an arithmetic progression is S_n = (n)/(2)(a_1 + a_n). Substitute the values: S_100 = (100)/(2)(101 + 200). S_100 = 50(301). S_100 = 15050. 101+102+103++200 = 15050 The sum of the series is 15050.