Given : 9 × (9th term) = 13 × (13th term)

To prove: 22nd term is 0

9 × (a + 8d) = 13 × (a + 12d)

9a + 72d = 13a + 156d

– 4a = 84d

a = – 21d …..Equation 1

Also 22nd term is given by

a + 21d

Using equation 1 we get

– 21d + 21d = 0

Hence proved 22nd term is 0.