Question

If five times the fifth term of an A.P. is equal to 8 times its eight term, show that its 13^th term is zero

Answer 1

Let a₁ , a₂ , a₃ , ….. , an, …. be the A.P. with its first term = a and common difference = d.

It is given that 5a₅ = 8a₈

⇒ 5(a + 4d) = 8 (a + 7d)

⇒ 5a + 20d = 8a + 56d ⇒ 3a + 36d = 0

⇒ 3(a + 12d) = 0 ⇒ a + 12d = 0

⇒ a + (13 – 1) d = 0 ⇒ a₁₃ = 0