Question

if 10 times the 10th term of an A.P is equal to 3 times the 3rd term, show that 3rd term of an A.P is zero ?

Answer 1

a10 = a + 9d

a3 = a + 2d


10 ( a + 9d ) = 3 ( a + 2d )

10a + 90d = 3a + 6d

10a - 3a = 6d - 90d

7a = - 84d

a = - 12d

Now ,

a3 = a + 2d

= - 12d + 2d

= - 10d