Question

if the 3rd and the 9th term of an AP are 4 and -8 respectively. Which term of the AP is zero

Answer 1

nth term of an AP an = a + (n - 1) * d.

Let the first term be a and the common difference be d.

(i)

Given that third term of an AP = 4.

⇒ a₃ = a + (3 - 1) * d

⇒ 4 = a + 2d    

(ii)

Given that 9th term of an AP is -8.

⇒ a₉ = a + (9 - 1) * d

⇒ -8 = a + 8d

On solving (1) & (2), we get

⇒ a + 2d = 4

⇒ a + 8d = -8

   ----------------

          -6d = 12

             d = -2.

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

⇒ a + 2d = 4

⇒ a + 2(-2) = 4

⇒ a - 4 = 4

⇒ a = 8.

Now,

Given that nth term will be 0.

⇒ a + (n - 1) * d = 0

⇒ 8 + (n - 1) * (-2) = 0

⇒ 8 - 2n + 2 = 0

⇒ 10 - 2n = 0

⇒ 10 = 2n

⇒ n = 5.

Therefore, 5th term of the AP is zero.

Hope it helps!

Answer 2

HEY MATE HERE IS YOUR ANSWER

$<b><big >$

Given that nth term will be 0.

Therefore,

➡️ a + (n-1) d = 0

➡️ 8 + (n-1) (-2) = 0

➡️ 8 - 2n + 2 = 0

➡️ 10 - 2n = 0

➡️ 10 = 2n

➡️ n = 10/2

➡️ n = 5

THEREFORE, 5TH TERM OF THE "AP" OS ZERO.




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