Binomial Theorem
AP of Binomial Coefficients
nta_pyq_2024_apr
Grade 11
Question:
If the coefficients of $x^4$, $x^5$ and $x^6$ in the expansion of $(1+x)^n$ are in arithmetic progression, then the maximum value of $n$ is:
Step-by-Step Solution
Key Concept: $2\binom{n}{5}=\binom{n}{4}+\binom{n}{6}\Rightarrow n^2-21n+98=0\Rightarrow n=7$ or $14$.
$n=7$ or $14$. Max $=14$.
Correct Answer: 4