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 — let's continue with Activity 3. Predict how many matchsticks will be needed for Pattern 10. Explain how you get your answer. Step 1: Recall the general rule for the number of matchsticks. From our previous analysis of Activity 3.1, the number of matchsticks used for the whole shape in Pattern n is given by the formula T_n = 2n(n+1). Step 2: Substitute n=10 into the formula. T_10 = 2(10)(10+1) T_10 = 20(11) T_10 = 220 Step 3: Explain the calculation. The number of matchsticks for Pattern 10 is found by substituting n=10 into the general rule T_n = 2n(n+1), which results in 2(10)(10+1) = 20(11) = 220. Number of matches in pattern 10 = 220 3.3 Write down the general rule for the pattern in the form T_n= Step 1: Identify the correct general rule. Based on the pattern observed in Activity 3.1, the number of matchsticks for Pattern n is given by the formula 2n(n+1). The rule you wrote, T_n = 3n+2, is incorrect for this pattern. For example, for Pattern 1, it would give 3(1)+2=5, but the actual number of matches is 4. Step 2: State the correct general rule. T_n = 2n(n+1) What's next?