If 9 times the 9th term of an AP is equal to 13 times the 13th term, s

1.	If 9 times the 9th term of an AP is equal to 13 times the 13th term, show that its 22nd term is 0.
Answer» Given: 9 × (9^th term) = 13 × (13^th term) To prove: 22^nd term is 0 9 × (a + 8d) = 13 × (a + 12d) 9a + 72d = 13a + 156d - 4a = 84d a = - 21d …..Equation 1 Also 22^nd term is given by a + 21d Using equation 1 we get - 21d + 21d = 0 Hence proved 22^nd term is 0.

If 9 times the 9th term of an AP is equal to 13 times the 13th term, show that its 22nd term is 0.

Answer»

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

To prove: 22^nd term is 0

9 × (a + 8d) = 13 × (a + 12d)

9a + 72d = 13a + 156d

- 4a = 84d

a = - 21d …..Equation 1

Also 22^nd term is given by

a + 21d

Using equation 1 we get

- 21d + 21d = 0

Hence proved 22^nd term is 0.