Question

If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero?

Options

• 5^th

• 4^th

• 3^rd

• 6^th

Answer 1

5^th

Explanation:-

It is given that 3rd and 9th term of AP are 4 and -8 respectively.

It means a₃ = 4 and a₉ = -8

Where, a₃ and a₉ are third and ninth terms respectively.

Using formula a_n = a + (n - 1)d to find n^th term of arithmetic progression, we get

4 = a + (3 - 1)d

⇒ 4 = a + 2d    ...(i)

-8 = a + (9 - 1)d

⇒ -8 = a + 8d      ...(ii)

From equation (i) we have a = 4 - 2d

Substituting in equation (ii) , we have

-8 = 4 - 2d + 8d

⇒ -12 = 6d

⇒ d = `-12/6` = −2

Solving for (a) , we get

⇒ -8 = a - 16

⇒ a = 8

Therefore, first term a = 8 and Common Difference d = -2

We know a_n = a + (n - 1)d (where a_n is the n^th term)

Finding value of n where an = 0

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

⇒ 0 = 8 - 2n + 2

⇒ 0 = 10 - 2n

⇒ 2n = 10

⇒ n = `10/2` = 5

Therefore, 5th term is equal to 0.