Binomial Theorem
Greatest Term in Sequence
nta_pyq_2023_apr
Grade 11
Question:
If $a_\alpha$ is the greatest term in the sequence $a_n=\dfrac{n^3}{n^4+147}$, $n=1,2,3,\ldots$, then $\alpha$ is equal to ______.
Step-by-Step Solution
Key Concept: Treat $f(x)=\frac{x^3}{x^4+147}$ as a continuous function and find its maximum by setting $f'(x)=0$.
$f(5)=\frac{125}{772}>f(4)=\frac{64}{403}$. Maximum at $\alpha=5$.
Correct Answer: 5