An important and exam oriented question from arithmetic progression chapter as it was already asked in previous year paper of 2015 in which we have been asked to prove that 25th term is 0, if 10 times the 10th term of an AP is equal to 15 times the 15th term.
Book – RS Aggarwal, class 10, Arithmetic Progression, chapter 5A, question no 33
According to question,
10(a+9d)=15(a+14d)
10a+90d=15a+210d
15a+210d-10a-90d=0
5a+120d=0
5(a+24d)=0
a+24d=0
therefore 25th term is zero
hence proved.