18 The 4th term of an AP is zero. Prove thatthe 25th term of the AP is

1.	18 The 4th term of an AP is zero. Prove thatthe 25th term of the AP is three times its[CBSE 2016]11th term.
Answer» Given a^4 = 0 That is (a + 3d) = 0 ⇒ a = - 3d ........... (1) nth term of AP is given by an = a + (n – 1)d a^11 = a + 10d = – 3d + 10d = 7d [From (1)] a^25 = a+ 24d = – 3d + 24d = 21d [From (1)] = 3 x 7d Hence a^25 = 3 x a^11

18 The 4th term of an AP is zero. Prove thatthe 25th term of the AP is three times its[CBSE 2016]11th term.

Answer»

Given a^4 = 0

That is (a + 3d) = 0

⇒ a = - 3d ........... (1)

nth term of AP is given by an = a + (n – 1)d

a^11 = a + 10d = – 3d + 10d = 7d [From (1)]

a^25 = a+ 24d = – 3d + 24d = 21d [From (1)]

= 3 x 7d

Hence a^25 = 3 x a^11