Answer :

Let first term be a and common difference be d.

We know that, a_{n} = a + (n - 1)d

Where,

a = First term of AP

d = Common difference of AP

and no of terms is ‘n’

∴ a_{3} = a + (3 - 1)d

⇒ 4 = a + 2d …(i)

and a_{9} = a + (9 - 1)d

⇒ -8 = a + 8d …(ii)

On solving eq. (i) and (ii), we get,

a = 8 and d = -2

Let the n^{th} term be zero.

⇒ a_{n} = a + (n - 1)d

⇒ 0 = 8 + (n - 1) × (-2)

⇒ 0 = 8 – 2n -2(-1)

⇒ 0 = 8 – 2n + 2

⇒ -10 = – 2n⇒ n = 5

Hence, 5^{th} will be zero.

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