#### 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

#### Solution

Let a_{1} , a_{2} , a_{3} , ….. , an, …. be the A.P. with its first term = a and common difference = d.

It is given that 5a_{5} = 8a_{8}

⇒ 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 ⇒ a_{13} = 0

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Solution If five times the fifth term of an A.P. is equal to 8 times its eight term, show that its 13th term is zero Concept: Arithmetic Progression.