Answer 1

Nine times ninth term = Fifteen times fifteenth term

9t₉ = 15t₁₅

9(a + 8d) = 5(a + 14d)

9a + 72d = 15a + 210

15a + 210d – 9a – 72d = 0

⇒ 6a + 138 d = 0

⇒ 6(a + 23 d) = 0

⇒ 6(a + (24 – 1)d) = 0

⇒ 6t₂₄ = 0.

Hence it is proved.