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
b) 15 Step 1: Use the sum formula for an arithmetic progression to find the first term (a_1). The sum of n terms is given by S_n = (n)/(2)(a_1 + a_n). Given S_10 = 120, n = 10, and a_10 = 21. 120 = (10)/(2)(a_1 + 21) 120 = 5(a_1 + 21) Divide both sides by 5: (120)/(5) = a_1 + 21 24 = a_1 + 21 Subtract 21 from both sides: a_1 = 24 - 21 a_1 = 3 Step 2: Use the formula for the n-th term to find the common difference (d). The n-th term is given by a_n = a_1 + (n-1)d. Given a_10 = 21, a_1 = 3, and n = 10. 21 = 3 + (10-1)d 21 = 3 + 9d Subtract 3 from both sides: 21 - 3 = 9d 18 = 9d Divide both sides by 9: d = (18)/(9) d = 2 Step 3: Calculate the first three terms of the arithmetic progression. The first term is a_1 = 3. The second term is a_2 = a_1 + d = 3 + 2 = 5. The third term is a_3 = a_2 + d = 5 + 2 = 7. Step 4: Find the sum of the first three terms. The sum of the first three terms is S_3 = a_1 + a_2 + a_3. S_3 = 3 + 5 + 7 S_3 = 15 The sum of the first three terms is 15. Send me the next one 📸