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
3. Write the required term in each of these patterns: a) In the number pattern 1; 4; 9; ..., find the fifth term. Step 1: Identify the pattern. The terms are perfect squares: 1^2, 2^2, 3^2, . Step 2: Determine the fifth term. The fifth term will be 5^2. 5^2 = 25 The fifth term is 25. b) In the number pattern 2 000; 200; 20; ..., find the fourth term. Step 1: Identify the pattern. Each term is divided by 10 (or multiplied by (1)/(10)). Step 2: Calculate the fourth term. 20 ÷ 10 = 2 The fourth term is 2. c) In the number pattern 10(1)/(2); 10; 9(1)/(2); 9; ..., find the sixth term. Step 1: Identify the pattern. Each term decreases by (1)/(2). Step 2: List the terms to find the sixth term. The given terms are: T_1 = 10(1)/(2), T_2 = 10, T_3 = 9(1)/(2), T_4 = 9. T_5 = 9 - (1)/(2) = 8(1)/(2) T_6 = 8(1)/(2) - (1)/(2) = 8 The sixth term is 8. d) In the number pattern 1; 2; 4; 7; ..., find the sixth term. Step 1: Identify the pattern of differences between consecutive terms. 2 - 1 = 1 4 - 2 = 2 7 - 4 = 3 The differences are increasing by 1 each time. Step 2: Calculate the next terms using this pattern. The next difference will be 4, so T_5 = 7 + 4 = 11. The next difference will be 5, so T_6 = 11 + 5 = 16. The sixth term is 16. e) In the number pattern 1; 0,9; 0,8; 0,7 ..., find the seventh term. Step 1: Identify the pattern. Each term decreases by 0.1. Step 2: List the terms to find the seventh term. The given terms are: T_1 = 1, T_2 = 0.9, T_3 = 0.8, T_4 = 0.7. T_5 = 0.7 - 0.1 = 0.6 T_6 = 0.6 - 0.1 = 0.5 T_7 = 0.5 - 0.1 = 0.4 The seventh term is 0.4. That's 2 down. 3 left today — send the next one.