AP EAMCET · Maths · Sequences and Series
If the eleventh term in the binomial expansion of \((x+a)^{15}\) is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is
- A \(7^{\text {th }}\) term
- B \(8^{\text {th }}\) term
- C \(9^{\text {th }}\) term
- D \(10^{\text {th }}\) term
Answer & Solution
Correct Answer
(B) \(8^{\text {th }}\) term
Step-by-step Solution
Detailed explanation
From the given condition \(T_{11}=\sqrt{T_8 T_{12}}\) \(\begin{aligned} & \Rightarrow\left({ }^{15} C_{10} x^5 a^{10}\right)=\left({ }^{15} C_7 x^8 a^7\right)\left({ }^{15} C_{11} x^4 a^{11}\right) \\ & \Rightarrow \frac{x}{a}=\sqrt{\frac{77}{75}} \end{aligned}\) Now, greatest…
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