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Mathematics

If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively. Which term of it is zero ?

AP GP

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Answer

Let first term be a and common difference be d.

Given,

⇒ 3rd term = 4

⇒ a3 = 4

⇒ a + 2d = 4

⇒ a = 4 - 2d ……..(Eq. 1)

Given,

⇒ 9th term = -8

⇒ a9 = -8

⇒ a + 8d = -8

⇒ a = -8 - 8d ……..(Eq. 2)

From Eq. 1 and Eq. 2,

⇒ 4 - 2d = -8 - 8d

⇒ -2d + 8d = -8 - 4

⇒ 6d = -12

⇒ d = −126\dfrac{-12}{6} = -2.

Substituting value of d in Eq. 1, we get :

⇒ a = 4 - 2d = 4 - 2(-2) = 4 + 4 = 8.

Let nth term be zero.

⇒ an = 0

⇒ a + (n - 1)d = 0

⇒ 8 + (n - 1)(-2) = 0

⇒ 8 - 2n + 2 = 0

⇒ 2n = 10

⇒ n = 102\dfrac{10}{2} = 5.

Hence, 5th term will be 0.

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