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 sequence of numbers. The first hundred odd numbers form an arithmetic progression: 1, 3, 5, . Step 2: Determine the number of terms and the first term. We need the sum of the first hundred odd numbers, so the number of terms n = 100. The first term a_1 = 1. Step 3: Determine the last term. The n-th odd number is given by the formula 2n - 1. For the 100th odd number, a_100 = 2(100) - 1 = 200 - 1 = 199. Step 4: Calculate the sum of the arithmetic progression. The sum of an arithmetic progression is given by the formula S_n = (n)/(2)(a_1 + a_n). Substitute the values: S_100 = (100)/(2)(1 + 199) S_100 = 50(200) S_100 = 10000 Alternatively, the sum of the first n odd numbers is n^2. For n=100: S_100 = 100^2 S_100 = 100 × 100 S_100 = 10000 The sum of the first hundred odd numbers is 10000. Comparing this with the given options: A 200 B 500 C 1 000 D 10 000 E 100 000 The correct option is D. The final answer is 10 000. Send me the next one 📸