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, Kyekyeku, let's confirm those answers. a) The 5th term Step 1: Recall the first term and common ratio. From the previous calculations, the first term is a=10 and the common ratio is r=(3)/(5). Step 2: Calculate the 5th term using the formula T_n = ar^n-1. T_5 = 10 ((3)/(5))^5-1 T_5 = 10 ((3)/(5))^4 T_5 = 10 × (81)/(625) T_5 = (810)/(625) T_5 = (162)/(125) The 5th term is (162)/(125). b) The sum of the first four terms Step 3: Calculate the sum of the first four terms using the formula S_n = (a(1-r^n))/(1-r). S_4 = (10(1-(3)/(5))^4)1-(3)/(5) S_4 = (10(1-81)/(625))(2)/(5) S_4 = (10(625-81)/(625))(2)/(5) S_4 = (10(544)/(625))(2)/(5) S_4 = 10 × (544)/(625) × (5)/(2) S_4 = (5440 × 5)/(1250) S_4 = (27200)/(1250) S_4 = (544)/(25) The sum of the first four terms is (544)/(25). That's 2 down. 3 left today — send the next one.