If 9 ^thterm of an A.P. is zero, prove that its 29 ^thtermis double the 19 ^thterm.

Given: T ₉ = 0

To Prove: T ₂₉ = 2T ₁₉

We know that,

T _n = a ₁ + (n – 1)d

⇒ T ₉ = a ₁ + (9 – 1)d

⇒ T ₉ = a ₁ + 8d

⇒ a ₁ + 8d = 0

Now,

T ₂₉ = a ₁ + (29 – 1)d = a ₁ + 28d = a ₁ + 8d + 20d = 0 + 20d = 20d
T ₁₉ = a ₁ + (19 – 1)d = a ₁ + 18d = a ₁ + 8d + 10d = 0 + 10d = 10d

⇒ T ₂₉ = 2T ₁₉ .
Hence, Proved