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
Okay ~Gracina~, let's calculate Mr. Ade's total debt. This problem describes an arithmetic progression, where Mr. Ade's monthly borrowing increases by a constant amount. Step 1: Identify the first term, common difference, and number of terms. The sequence of borrowings is ₦ 530.00, ₦ 545.00, ₦ 560.00, ... The first term (a) is the amount borrowed in the first month: a = 530 The common difference (d) is the difference between consecutive terms: d = 545 - 530 = 15 d = 560 - 545 = 15 The total debt is for "a year", which means 12 months. So, the number of terms (n) is: n = 12 Step 2: Use the formula for the sum of an arithmetic progression. The sum of the first n terms of an arithmetic progression (S_n) is given by the formula: S_n = (n)/(2)[2a + (n-1)d] Step 3: Substitute the values and calculate the total debt. Substitute a=530, d=15, and n=12 into the formula: S_12 = (12)/(2)[2(530) + (12-1)15] S_12 = 6[1060 + (11)15] S_12 = 6[1060 + 165] S_12 = 6[1225] S_12 = ₦ 7350.00 That's 2 down. 3 left today — send the next one.