Question

if the third term and ninth term of AP are 4 and -8 which term of AP is 0​

Answer 1

Answer:-

n = 5

Given :-

$a_3 = 4$

$a_9 = -8$

To find :-

Which term if AP will be 0.

Solution:-

Let nth term of AP will be 0.

Then, $a_n = 0$

$a_3 = 4$

→$a + 2d = 4--------eq.1$

Also,

$a_9 = -8$

→$a + 8d = -8--------eq.2$

Subtract eq. 1 and eq. 2

→$a +2d -(a+8d) = 4-(-8)$

→$a - a +2d -8d = 12$

→$-6d = 12$

→$d = \dfrac{-12}{6}$

→$d = -2$

a + 2d = 4

a + 2.(-2) = 4

a -4 = 4

a = 4 + 4

a = 8

Now,

$a_n = 0$

→$a + (n-1) d = 0$

→$8 +(n-1) -2=0$

→$8 -2n +2 = 0$

→$10 = 2n$

→$n = \dfrac{10}{2}$

→$n = 5$

hence,5th term of AP will be 0.

Answer 2

GIVEN :

Third term of an AP = 4

a + 2d = 4 ------(1)

Ninth term of an AP = -8

a + 8d = -8 ------(2)

Solve eq - (1) and (2) to find common difference (d).

a + 2d = 4

a + 8d = -8

(-) (-) (+)

----------------

-6d = 12

d = 12/-6

d = -2

Common Difference (d) = -2

Substitute d in any equation to find first term (a)

a + 2(-2) = 4

a - 4 = 4

a = 4 + 4

a = 8

First Term (a) = 8

We know that,

In an AP nth term = an = a + (n - 1)d

8 + (n - 1)-2 = 0

8 - 2n + 2 = 0

10 - 2n = 0

10 = 2n

n = 10/2

n = 5

Therefore, 0 is the fifth of AP.