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
Step 1: Write the given information using the formula for the n-th term of a Geometric Progression, a_n = ar^n-1, where a is the first term and r is the common ratio. The second term is 9: a_2 = ar^2-1 = ar = 9 (1) The fourth term is 81: a_4 = ar^4-1 = ar^3 = 81 (2) Step 2: Divide equation (2) by equation (1) to eliminate a and solve for r. (ar^3)/(ar) = (81)/(9) r^2 = 9 Step 3: Solve for r. r = ±sqrt(9) r = ± 3 The common ratio can be either 3 or -3. The common ratio is ± 3 Send me the next one 📸