An Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.
Here the nth term of AP is n times and the second nth term of AP is n times you have to show that the further nth term is zero.
This is the Question Number 27 Exercise 11 A of RS Aggarwal Solution.
Deepak BoraNewbie
If 10 times the 10th term of an AP is equal to 15 times the 15th term show that its 25th term is zero.
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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.