If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero? Options: A . &nbsp5th term B . &nbsp4th term C . &nbsp3rd term D . &nbsp6th term

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

Question

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

Options:

A . 5th term

B . 4th term

C . 3rd term

D . 6th term

Answer: Option A
:
A
Given,

a_{3} = 4

and

a_{9} = - 8,

where

a_{3}

and

a_{9}

are the third and ninth terms of an AP respectively.
Using the formula for

n^{th}

term of an AP with first term

a

and common difference

d,

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

we get

a_{3} = a + (3 - 1) d

and

a_{9} = a + (9 - 1) d .

\Rightarrow 4 = a + 2 d . . . (i)

- 8 = a + 8 d . . . (i i)

Substituting the value of

a

from equation (i) in equation (ii),we have

- 8 = 4 - 2 d + 8 d

\Rightarrow - 12 = 6 d

\Rightarrow d = - \frac{12}{6} = - 2

Solving for

a,

we get

- 8 = a - 16.

\Rightarrow a = 8

Therefore, the first term of the APis8and common difference is −2.
Let the

n^{th}

term of the AP be zero.
i.e.,

a_{n} = 0

a + (n - 1) d = 0

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

\Rightarrow 8 - 2 n + 2 = 0

\Rightarrow 2 n = 10

\Rightarrow n = \frac{10}{2} = 5

Therefore, the

5^{th}

term of the AP is equal to0.

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