Question

F 10 times the 10th term of an ap is equal to 15 tim es its 15th term, show that its 25th term is zero

Answer 1

Suppose , 25th term of an AP = 0


a + 24d = 0



a = -24d.






Given that : 10 ( 10th term ) = 15 ( 15th term )



=> 10 ( a + 9d ) = 15 ( a + 14d )



=> 10 ( -24d + 9d ) = 15 ( -24d + 14d )




=> 10 × -15d = 15 × -10d



=> -150d = -150d



=> 150d = 150d. ( Equal )


Hence,


25th term of the given AP will be equal to 0.

Answer 2

let 25th term = 0

a + 24d = 0

a = -24d


10(10th term ) = 15 ( 15th term )


10 ( a + 9d ) = 15 ( a + 14d )


10 ( -24d + 9d ) = 15 ( -24d + 14d )


150d = 150d