Final answer:
To find the ratio of the 10th terms of two arithmetic progressions (APs) given their sum ratios, we need to determine the formula for the sum of the n terms of each AP. Using the formulas for the sum of the n terms, we can set up an equation with the given ratio and solve for the ratio of the 10th terms.
Step-by-step explanation:
To find the ratio of the 10th terms of two arithmetic progressions (APs) given their sum ratios, we need to determine the formula for the sum of the n terms of each AP.
Let's start with the first AP. The sum of the first n terms of an AP is given by the formula S1 = n(2a1 + (n-1)d1)/2, where a1 is the first term and d1 is the common difference.
Similarly, the sum of the first n terms of the second AP is given by the formula S2 = n(2a2 + (n-1)d2)/2.
Given that the ratio of S1 to S2 is (7n + 1) : (4n + 27), we can set up the equation (7n + 1)/(4n + 27) = T1/T2, where T1 and T2 represent the 10th terms of the two APs.
To find the ratio of the 10th terms, we substitute n = 10 into the equation and solve for T1/T2.
By solving the equation, we can find the ratio of the 10th terms of the two APs.