Question

If 3rd and 9th terms of ap are 4 and -8 respectively which term of ap is zero

Answer 1

Answer:

a3=a+2d=4

or, a=4-2d

and a9=a+8d=-8

or, 4-2d+8d=-8

or, 6d=-12

d=-2

a=4-2(-2)

=4+4=8

now, let an=0

or, a+(n-1) d=0

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

(n-1) =-8/-2

n=4+1=5

thus, required term is 5th term

Answer 2

a3 =4

a9 = -8

a + 2d = 4 eq 1

a + 8d = -8 eq 2

subtract both eq1 and 2 we get

d = -2

that d = -2 and substitute in eq 1 we get

a + 2 × -2 = 4

a = 8

an = 0

an = a +( n-1) d

0 = 8 + (n-1) -2

-8 = (n-1) -2

-8/-2 = n-1

4 = n-1

n = 5

so 5th term is 0