Question

If the 9th term of an A.P is 0, prove that its 29th term is double the 19th term.

Answer 1

a9 = 0
a + 8d = 0
a = -8d ...... (1)

Now, to prove,
a29 = 2a19
a + 28d = 2(a + 18d)
a + 28d = 2a + 36d
-8d + 28d = -16d + 36d
20d = 20d

Since LHS=RHS, hence proved.

Answer 2

Answer:

a9 = 0

a + 8d = 0

a = -8d ...... (1)

Now, to prove,

a29 = 2a19

a + 28d = 2(a + 18d)

a + 28d = 2a + 36d

-8d + 28d = -16d + 36d

20d = 20d

Since LHS=RHS, hence proved.