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: Determine the rule for the pattern. Observe the given values for "Number of match sticks" (output) corresponding to "Stage" (input): • Stage 1 gives 5 match sticks • Stage 2 gives 9 match sticks • Stage 3 gives 13 match sticks • Stage 4 gives 17 match sticks Calculate the difference between consecutive output values: 9 - 5 = 4 13 - 9 = 4 17 - 13 = 4 The common difference is 4. This indicates a linear relationship, which can be expressed as T_n = an + b, where a is the common difference. So, the rule is of the form T_n = 4n + b. Using the first pair (Stage 1, 5 match sticks): 5 = 4(1) + b 5 = 4 + b b = 1 The rule for the number of match sticks at Stage n is T_n = 4n + 1. Step 2: Complete the table for the missing output value (1.4.1). The table asks for the number of match sticks at Stage 5. Using the rule T_n = 4n + 1 for n=5: T_5 = 4(5) + 1 = 20 + 1 = 21 The missing value for 1.4.1 is 21. Step 3: Complete the table for the missing input value (1.4.2). The table asks for the Stage number when the number of match sticks is 41. Set T_n = 41 and solve for n: 4n + 1 = 41 4n = 41 - 1 4n = 40 n = (40)/(4) n = 10 The missing value for 1.4.2 is 10. The completed table is: | Stage | 1 | 2 | 3 | 4 | 5 | 10 | |-----------------------|---|---|---|---|----|------| | Number of match sticks | 5 | 9 | 13| 17| 21 | 41 | The missing input value is 10. The missing output value is 21. Got more? Send 'em!