Question

Given that a, b, and n are positive integers where a is the first term, b is the second term, and n is the power of (ab)", and the first three terms in the binomial expression (ab)" are 729, 2916, and 4860. Find the values of a, b, and n.

Answer 1

To find the values of a, b, and n in the binomial expression (ab)^n, we can use the information provided. By analyzing the given terms and equations, we can solve for a, b, and n.

Step-by-step explanation:

To find the values of a, b, and n in the binomial expression (ab)^n, we need to analyze the given information.

1. We know that the first term in the expression is 729, which is equal to a^n. Therefore, a^3 = 729.
2. The second term is 2916, which is equal to n * a^(n-1) * b. Therefore, (3 * a^2 * b) = 2916.
3. The third term is 4860, which is equal to n * (n-1) * a^(n-2) * b^2. Therefore, (3*(3-1)*a^(3-2)*b^2) = 4860.

Based on these equations, we can solve for the values of a, b, and n.