Question

Find out the largest term of the sequence $\frac{1}{503},\frac{4}{524},\frac{9}{581},\frac{16}{692},....$

• A. $\frac{25}{875}$
• B. $\frac{36}{1148}$
• C. $\frac{49}{1529}$
• D. $\frac{64}{2036}$

Answer 1

Answer: (C)

$\frac{49}{1529}$

General term can be written as
$T_n=\frac{n^2}{500+3n^3}$
then, $\frac{d{T}_n}{dn}=\frac{n(1000-3n^3)}{(500+3n^3{)}^2}$
For max or min of $T_n$,
$\frac{d{T}_n}{dn}=0$
$\therefore n={\left(\frac{1000}{3}\right)}^{1/3}=6.933\approx 7$
Hence, $T_7$ is the largest term. So largest term in the given sequence is $\frac{49}{1529}$