If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.
10a10 = 15a15
10[a + (10 – 1)d] = 15[a + (15 – 1)d]
2a + 2(9)d = 3a + 3(14)d
-a = 42d – 18d
-a = 24d
a = -24d
a25 = a + 24d
= -24d + 24d
= 0