Question

9. If the 3rd and the 9th terms of an AP are 4 and - 8 respectively, which term of this ap is zero​

Answer 1

Given :-

◉ 3rd term and 9th term of an AP are 4 and -8 respectively.

To Find :-

◉ Which term of the given AP is 0.

Solution :-

We know,

⇒ aₙ = a + (n - 1)d

Given, 3rd & 9th term are 4 and -8 respectively.

⇒ a₃ = a + 2d

⇒ a + 2d = 4 ...(1)

Also,

⇒ a₉ = a + 8d

⇒ a + 8d = -8 ...(2)

Subtract (1) from (2), we get

⇒ a + 8d - a - 2d = -8 - 4

⇒ 6d = -12

⇒ d = -2

Substitute d = -2 in (1) , we have

⇒ a + 2×-2 = 4

⇒ a = 8

Now, that we have found the first term and the common Difference of AP, So

We can find the term which would be 0 by evaluating it to the nth term and finding the value of n,

⇒ aₙ = a + (n - 1)d

⇒ 8 + (n - 1)×-2 = 0

⇒ 8 - 2n + 2 = 0

⇒ 2n = 10

⇒ n = 5

Hence, The 5th term of the AP would be 0.