Binomial Theorem
Consecutive Terms in Ratio — Sum of Coefficients
nta_pyq_2023_apr
Grade 11
Question:
The sum of the coefficients of three consecutive terms in the binomial expansion of $(1+x)^{n+2}$, which are in the ratio $1:3:5$, is equal to
Step-by-Step Solution
Key Concept: Set up: $\frac{\binom{n+2}{r}}{\binom{n+2}{r-1}}=3$ and $\frac{\binom{n+2}{r+1}}{\binom{n+2}{r}}=\frac{5}{3}$. Solve for $r$ and $n$.
$n=5,\ r=2$. Sum $=\binom{7}{1}+\binom{7}{2}+\binom{7}{3}=63$.
Correct Answer: 2