Question

If the third th term and nineth term of an ap are 4and-8respectively which term of an ap will be zero

Answer 1

let first term of A. P = a

let common difference = d

nth term of A.P an = a + (n-1)d

third term of A.P = a3 = a + (3-1)d = 4

⇒ a + 2d = 4      ------------eq 1

9 term = a9 = a + ( 9-1 ) d = -8

⇒ a + 8d = -8    ---------------eq2

Subtracting eq 1 from eq 2

a + 8d - a - 2d = -8 - 4

6d = -12

d = -12/6 = -2

substituting value of d in eq1

⇒ a + (2×(-2))= 4

⇒ a  - 4 = 4

⇒ a = 8

we need n , when term is 0

⇒ 0 = a + ( n -1 ) d

⇒ 0 = 8 + (n-1) (-2)

⇒ -8/(-2) = n-1

⇒  n-1 = 4

⇒  n = 4 + 1 = 5

hence fifth term of A.P will be zero.

A.P is 8 , 6 , 4 , 2 , 0 , .....

Answer 2

Let the 1st term and common difference of the AP series be A & d respectively.
Now
4 = A + 2d
-8 = A + 8d
On solving we get d= -2 and A= 8
Now A/Q
0 = 8 + (n-1)(-2)
n =5
So 5th term will be 0