Question

If the \(7^{\text{th}}\) and \(8^{\text{th}}\) terms of the binomial expansion \[ (2a - 3b)^n \] are equal, then the value of \[ \frac{2a + 3b}{2a - 3b} \] is equal to:

• A. \( \frac{13 - n}{n + 1} \)
• B. \( \frac{n + 1}{13 - n} \)
• C. \( \frac{6 - n}{13 - n} \)
• D. \( \frac{n - 1}{13 - n} \)
• E. \( \frac{2n - 1}{13 - n} \)

Hint:

The ratio of consecutive terms is \( \frac{T_{r+1}}{T_r} = \frac{n-r+1}{r} \cdot \frac{y}{x} \). Setting this ratio to 1 (or -1 depending on the sign of terms) allows for a quick derivation of the relationship between the binomial components.

Answer 1

The Correct Option is B