Question

If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively, Which term of it is zero?

Answer 1

For an A.P

`t_3 = 4`

=> a +2d = 4 .....(i)

`t_9 = -8`

=> a + 8d = -8 ....(ii)

Substractinjg (i) from (ii) we get

6d = -12

=> d = -2

Substituting d = -2 in (i) we get

a + 2(-2) = 4

=> a - 4 = 4

=> a = 8

=> general term = `t_n = 8 + (n - 1)(-2)`

Let pth term of this A.P be 0

`=> 8 + (p - 1) xx (-2) = 0`

`=> 8 - 2p + 2 = 0`

=> 10 - 2p = 0

=> 2p = 10

=> p = 5

Thus 5th term of this A.P is 0.