Question

If the 3rd and the 9th terms of an A.P are 4 and -8 respectively, which tern of this A.P is zero​

Answer 1

4=a+2d

-8=a+8d

solving it,

d=-2

a=8

now,

0=8+(n-1) ×-2

find n...

Answer 2

Question :-

If the 3rd and the 9th terms of an A.P are 4 and -8 respectively, which tern of this A.P is zero

Solution :-

Given : An A.P whose

3rd term = a + 2d = 4 .............( 1 )

9th term = a + 8d = -8 ..............( 2 )

__________

( - ) -6d = 12

__________

⟹ d = 12/-6

⟹ d = -2

Substituting d = -2 in equation ( 1 ) we get

a + 2 × (-2) = 4

⟹ a - 4 = 4

⟹ a = 4 + 4 = 8

Let the nth term of the given A.P be equal to zero.

an = a + (n - 1) d

⟹ 0 = 8 + (n - 1) d

⟹ 0 = 8 - 2n + 2

⟹ 10 - 2n = 0

⟹ 2n = 10

⟹ n = 10/2

⟹ n = 5

∴ The 5th term of the given A.P is zero.