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.