If the sum of the first n terms of the series √3+√75+√243+√507+....is 435√3, then n equals.

The correct option is D
15 ⇒ √3[1+√25+√81+√169+..+Tn]=435√3
⇒√3[1+5+9+13+.Tn]=435√3
⇒Formula:Sn=n/2[2a+(n−1)d]
⇒√3×n/2[2+(n−1)4]=435√3
⇒2n+4n²−4n=870
⇒4n²−2n−870=0
⇒2n²−n−435=0
n=1±√1+4×2×435/4=1±√3481/4=1±59/4
⇒1+59/4=15; 1−59/4=−14.5
n cannot be negative
Hence,n=15