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
Given the arithmetic progression 7, 11, 15, 19, . Step 1: Identify the first term (a) and the common difference (d). The first term is a = 7. The common difference is d = 11 - 7 = 4. a) Find the tenth term. Step 2: Use the formula for the n-th term of an arithmetic progression, u_n = a + (n-1)d. For the tenth term, n=10. u_10 = 7 + (10-1)4 u_10 = 7 + (9)4 u_10 = 7 + 36 u_10 = 43 The tenth term is 43. b) Find the sum of the first twelve terms. Step 3: Use the formula for the sum of the first n terms of an arithmetic progression, S_n = (n)/(2)(2a + (n-1)d). For the sum of the first twelve terms, n=12. S_12 = (12)/(2)(2(7) + (12-1)4) S_12 = 6(14 + (11)4) S_12 = 6(14 + 44) S_12 = 6(58) S_12 = 348 The sum of the first twelve terms is 348. Send me the next one 📸