Q. 83.7( 10 Votes )

# If the 3^{rd} and the 9^{th} terms of an AP are 4 and -8 respectively, which term of this AP is zero?

Answer :

Given

a_{n} = 0, n = ?

3^{rd} term = 4

⇒ a + (3-1)d = 4 → __1__

9^{th} term = 73

⇒ a + (9-1)d = -8 → __2__

By subtracting the both equations we will get ‘d’

(a +2d) – (a+8d) = 4 – (-8)

-6d = 12

d = -2

By substituting “d” in equation __1__

a +2d = 4

a + (-2)2 = 4

a = 8

a_{n} = a+(n-1)d

0 = 8+(n-1)(-2)

-8 = (n-1)(-2)

4 = n-1

n = 5

∴ 0 is the 5^{th} term in the series.

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