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 first term, common difference, and number of terms. The given sequence is an arithmetic progression: 2, 5, 8, The first term is a = 2. The common difference is d = 5 - 2 = 3. We need to find the sum of the first 20 terms, so n = 20. Step 2: Use the formula for the sum of the first n terms of an arithmetic progression. The formula is: S_n = (n)/(2)[2a + (n-1)d] Step 3: Substitute the values into the formula. S_20 = (20)/(2)[2(2) + (20-1)3] Step 4: Calculate the sum. S_20 = 10[4 + (19)3] S_20 = 10[4 + 57] S_20 = 10[61] S_20 = 610 Step 5: Compare the result with the given options. The calculated sum is 610, which corresponds to option (C). The final answer is C. 3 done, 2 left today. You're making progress.