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.
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Here are the solutions to the questions: Question 19: Find the 7th term of G.P from the following sequence: 4, 8, 16, 32 Step 1: Identify the first term and the common ratio of the Geometric Progression (G.P.). The first term is a = 4. The common ratio r is found by dividing any term by its preceding term: r = (8)/(4) = 2 Step 2: Use the formula for the n-th term of a G.P., which is T_n = a · r^n-1. We need to find the 7th term, so n=7. T_7 = 4 · 2^7-1 T_7 = 4 · 2^6 Step 3: Calculate the value. T_7 = 4 · 64 T_7 = 256 The 7th term is 256. The correct option is (C). The final answer is C Question 20: If 2^2x+y = 32 and 2^x-y = 1, find the value of x and y. Step 1: Convert the exponential equations into linear equations by expressing both sides with the same base. For the first equation: 2^2x+y = 32 Since 32 = 2^5, we have: 2^2x+y = 2^5 Equating the exponents gives: 2x+y = 5 (Equation 1) For the second equation: 2^x-y = 1 Since 1 = 2^0, we have: 2^x-y = 2^0 Equating the exponents gives: x-y = 0 (Equation 2) Step 2: Solve the system of linear equations. From Equation 2, we can deduce: x = y Substitute x for y in Equation 1: 2x + x = 5 3x = 5 x = (5)/(3) Step 3: Find the value of y. Since x=y, then: y = (5)/(3) The values are x = (5)/(3) and y = (5)/(3). Upon reviewing the provided options, none of them exactly match the calculated values of x = (5)/(3) and y = (5)/(3). The final answer is x = (5)/(3), y = (5)/(3)