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: Analyze the given sequence and identify the known terms. The sequence is 5824, 5242, ?, 4247, 3823. Let the terms be T_1, T_2, T_3, T_4, T_5. T_1 = 5824 T_2 = 5242 T_3 = ? (the missing term) T_4 = 4247 T_5 = 3823 Step 2: Calculate the differences between consecutive known terms. The difference between T_1 and T_2: D_1 = T_1 - T_2 = 5824 - 5242 = 582 The difference between T_4 and T_5: D_4 = T_4 - T_5 = 4247 - 3823 = 424 Step 3: Identify the pattern relating each term to its difference. Observe the relationship between a term T_n and the difference D_n (which is T_n - T_n+1). For T_1 = 5824, the difference D_1 = 582. Notice that 582 is the number formed by the first three digits of 5824. This can be expressed using the floor function: T_1 / 10 = 5824 / 10 = 582. So, T_2 = T_1 - T_1 / 10 . Let's check this pattern for T_4: For T_4 = 4247, the difference D_4 = 424. Similarly, T_4 / 10 = 4247 / 10 = 424. So, T_5 = T_4 - T_4 / 10 . The established pattern is T_n+1 = T_n - T_n / 10 . Step 4: Apply the pattern to find the missing term T_3. Using the pattern for T_2 to find T_3: T_3 = T_2 - T_2 / 10 Substitute the value of T_2: T_3 = 5242 - 5242 / 10 T_3 = 5242 - 524 T_3 = 4718 Step 5: Verify the result by checking the next term in the sequence. If T_3 = 4718, then T_4 should follow the pattern: T_4 = T_3 - T_3 / 10 T_4 = 4718 - 4718 / 10 T_4 = 4718 - 471 T_4 = 4247 This calculated value of T_4 matches the given T_4 in the sequence, confirming the correctness of the pattern and the missing term. The missing term is 4718. 3 done, 2 left today. You're making progress.