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
I can see question 7 on the image. Here's the solution: 7) The sum of the first n terms of an arithmetic progression is given by S_n = n^2 + 3n. a) Find the first term. The first term, T_1, is equal to the sum of the first term, S_1. Step 1: Substitute n=1 into the formula for S_n. S_1 = (1)^2 + 3(1) S_1 = 1 + 3 S_1 = 4 The first term is 4. T_1 = 4 b) Find the common difference. To find the common difference, we need the first two terms. We already have T_1 = 4. Step 1: Find the sum of the first two terms, S_2. S_2 = (2)^2 + 3(2) S_2 = 4 + 6 S_2 = 10 Step 2: Find the second term, T_2, using S_2 = T_1 + T_2. T_2 = S_2 - S_1 T_2 = 10 - 4 T_2 = 6 Step 3: Calculate the common difference, d = T_2 - T_1. d = 6 - 4 d = 2 The common difference is 2. d = 2 c) Find the 10th term. The formula for the n-th term of an arithmetic progression is T_n = a + (n-1)d, where a is the first term and d is the common difference. Step 1: Substitute a=4, d=2, and n=10 into the formula. T_10 = 4 + (10-1)2 T_10 = 4 + (9)2 T_10 = 4 + 18 T_10 = 22 The 10th term is 22. T_10 = 22 3 done, 2 left today. You're making progress.