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
Part (a): Sum of all terms Step 1: Sum formula for an AP S_n = (n)/(2) [2a + (n-1)d] Step 2: Substitute n=2025, a=4, d=3 S_2025 = (2025)/(2) [2(4) + (2025-1)(3)] S_2025 = (2025)/(2) [8 + 2024 × 3] Step 3: Simplify inside brackets 2024 × 3 = 6072 8 + 6072 = 6080 S_2025 = (2025)/(2) × 6080 Step 4: Simplify (6080)/(2) = 3040 S_2025 = 2025 × 3040 Step 5: Compute 2025 × 3040 2000 × 3040 = 6\,080\,000 25 × 3040 = 76\,000 6\,080\,000 + 76\,000 = 6\,156\,000 6156000 Part (b): Last term Step 1: Last term formula l = a + (n-1)d Step 2: Substitute n=2025, a=4, d=3 l = 4 + (2025-1) × 3 l = 4 + 2024 × 3 Step 3: Simplify 2024 × 3 = 6072 4 + 6072 = 6076 6076