If nine times ninth term is equal to fifteen times fifteenth term, show that six times twenty fourth term is zero.

If nine times ninth term is equal to fifteen times fifteenth term, show that six times twenty fourth term is zero.

Solution :

9t9  = 15t15

9(a + 8d)  = 15(a + 14d)

9a + 72d  = 15a + 210 d 

15a - 9a + 210d - 72d  = 0

6a + 138d  = 0

6(a + 23d)  = 0

a + 23d  = 0

t24  = 0

Hence proved.