Mathematics - Sequence & Series Question with Solution | TestHub

$\sqrt{3} \left[1+\sqrt{25}+ \sqrt{81}+ \sqrt{169}+\dots \right]=435\sqrt{3}$

$\sqrt{3} \left[1+5+9+13+\dots T_n\right]=435\sqrt{3}$

$= \sqrt{3}\times \frac{n}{2}\left[2+\left(n-1\right)4\right]=435\sqrt{3}$

$=2n+4n^2-4n=870$

$=4n^2-2n-870=0$

$=2n^2-n-435=0$

$n=\frac{1\pm \sqrt{1+4\times 2\times 435}}{4}$

$=\frac{1\pm 59}{4}$$\because n$is$+ve$

$\therefore n=\frac{1+59}{4}=15$