Study the pattern below and answer the question that follows. Draw a table to represent stage 1 to stage 5. Describe the pattern in Question 7.1 in your own words

7.1 Step 1: Analyze the pattern to determine the number of shaded diamonds at each stage. Stage 1: 2 shaded diamonds Stage 2: 4 shaded diamonds Stage 3: 6 shaded diamonds Stage 4: 8 shaded diamonds The number of shaded diamonds increases by 2 for each subsequent stage. This means the number of diamonds is 2 × stage number. Step 2: Calculate the number of shaded diamonds for stage 5. For stage 5, the number of diamonds will be 2 × 5 = 10. Step 3: Create the table. |c|c| Stage & Number of Shaded Diamonds \\ 1 & 2 \\ 2 & 4 \\ 3 & 6 \\ 4 & 8 \\ 5 & 10 \\ 7.2 The pattern shows that the number of shaded diamonds increases by two for each new stage. Specifically, the number of shaded diamonds is always double the stage number. 8.1 Step 1: Find the common difference between consecutive terms in the sequence. The given numbers are 5, 8, 11, 14. The differences are: 8 - 5 = 3 11 - 8 = 3 14 - 11 = 3 The common difference d = 3. Step 2: Use the formula for the n-th term of an arithmetic sequence, T_n = a + (n-1)d, where a is the first term and d is the common difference. Here, a = 5 and d = 3. Substitute these values into the formula: T_n = 5 + (n-1)3 Step 3: Simplify the expression to find the relationship. T_n = 5 + 3n - 3 T_n = 3n + 2 The relationship is T_n = 3n + 2. 8.2 Step 1: Use the rule found in question 8.1, which is T_n = 3n + 2. We need to find the 20^th number, so substitute n = 20 into the rule. T_20 = 3(20) + 2 Step 2: Calculate the value of T_20. T_20 = 60 + 2 T_20 = 62 The 20^th number is 62. Send me the next one 📸