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
The formula for the n-th term of a Geometric Progression (GP) is T_n = ar^n-1, where a is the first term and r is the common ratio. Step 1: Identify the given values. The 8th term (T_8) is -(7)/(32). The first term (a) is 28. The number of terms (n) is 8. Step 2: Substitute the given values into the formula for the 8th term. T_8 = ar^8-1 -(7)/(32) = 28r^7 Step 3: Solve for the common ratio r. Divide both sides by 28: r^7 = (-7)/(32)28 r^7 = -(7)/(32 × 28) Simplify the fraction: r^7 = -(1)/(32 × 4) r^7 = -(1)/(128) Step 4: Find the 7th root of -(1)/(128). Since 2^7 = 128, we have: r^7 = -((1)/(2))^7 r = -(1)/(2) The common ratio is -(1)/(2). 3 done, 2 left today. You're making progress.