Final answer:
To find the ratio of the 11th terms of two arithmetic series, we need to find the formulas for the sums of the two series and then find the ratio of those sums. The correct ratio is (c) 7:4.
Step-by-step explanation:
To find the ratio of the 11th terms of two arithmetic series, we need to find the formulas for the sums of the two series and then find the ratio of those sums.
Let's assume the first series has a common difference of d1 and the second series has a common difference of d2.
The formula for the sum of an arithmetic series is S = (n/2)(2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.
Using this formula, we can set up the ratio equation: (n/2)(2a1 + (n-1)d1) / (n/2)(2a2 + (n-1)d2) = (7n + 1) / (4n + 27), where a1 and a2 are the first terms of the two series.
By comparing the coefficients of the n terms on both sides, we can solve for the ratio of the common differences d1/d2. Once we have that ratio, we can find the ratio of the 11th terms by multiplying it by the ratio of the first terms.
The correct ratio is (c) 7:4.