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
You're on a roll — Step 1: Identify the pattern in the distances traveled. The distance traveled in the 1st second is 10 feet. The distance traveled in the 2nd second is 25 feet. The distance traveled in the 3rd second is 40 feet. Let's find the difference between consecutive distances: 25 - 10 = 15 40 - 25 = 15 Since the difference is constant, this is an arithmetic progression with the first term a_1 = 10 and the common difference d = 15. Step 2: Use the formula for the n-th term of an arithmetic progression. The formula for the n-th term is a_n = a_1 + (n-1)d. We need to find the distance traveled during the 7th second, so n=7. Step 3: Calculate the distance for the 7th second. Substitute a_1 = 10, d = 15, and n=7 into the formula: a_7 = 10 + (7-1) × 15 a_7 = 10 + (6) × 15 a_7 = 10 + 90 a_7 = 100 The ball will travel 100 feet during the 7th second. 100 feet What's next?