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
Let the three numbers in the Geometric Progression (GP) be a, ar, and ar^2, where a is the first term and r is the common ratio. Step 1: Identify the given values. The first term is a = 5. The third term is ar^2 = 245. Step 2: Substitute the value of a into the equation for the third term to find the common ratio r. 5r^2 = 245 Divide both sides by 5: r^2 = (245)/(5) r^2 = 49 Step 3: Solve for r. Take the square root of both sides: r = ±sqrt(49) r = ± 7 There are two possible values for the common ratio: r=7 and r=-7. Step 4: Calculate the middle number (ar) for each possible value of r. Case 1: If r = 7 The middle number is ar = 5 × 7 = 35. Case 2: If r = -7 The middle number is ar = 5 × (-7) = -35. The two possible values for the middle number are 35 and -35. That's 2 down. 3 left today — send the next one.