Question

If 5 times the fifth term of an AP is equal to 8 times its eight term, show that its 13^th term is zero.

Answer 1

Let a₁ , a₂ , a₃ , ….. , a_n, …. 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

Answer 2

Let the first term of AP is a and common difference of AP is d.

Therefore, the fifth term of given AP is a₅ = a + 4d

And the eight term of AP is a₈ = a + 7d.

Given that 5 times the fifth term of AP is equal to 8 times its eight term.

Hence, 13^th term of given AP is 0.