This is the basic and conceptual question from arithmetic progression chapter in which we have been asked to find 25th term if the sum of the first 14 terms of an AP is 1505 and its first term is 10.
Book RS Aggarwal, Class 10, chapter 5C, question no 40
Sum, Sn=n/2[2a+(n−1)d]
Given a=10
⇒S14=14/2[2(10)+(14−1)d]=1505
⇒1505=7[20+13d]
⇒1505=140+91d
⇒d=15
⇒nth term Tn=a+(n−1)d
⇒T25=10+(25−1)15
=10+24×15
=370