If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?

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#### Solution

Given that,

a_{3} = 4

a_{9} = −8

We know that,

a_{n} = a + (n − 1) d

a_{3} = a + (3 − 1) d

4 = a + 2d (I)

a_{9} = a + (9 − 1) d

−8 = a + 8d (II)

On subtracting equation (I) from (II), we obtain

−12 = 6d

d = −2

From equation (I), we obtain

4 = a + 2 (−2)

4 = a − 4

a = 8

Let n^{th} term of this A.P. be zero.

a_{n }= a + (n − 1) d

0 = 8 + (n − 1) (−2)

0 = 8 − 2n + 2

2n = 10

n = 5

Hence, 5^{th} term of this A.P. is 0.

Concept: nth Term of an AP

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