Question

If the 3^rd and the 9^th term of an A.P. be 4 and –8 respectively, find which term is zero?

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

Answer 1

For an A.P., a

t₃ = 4

`=>` a + 2d = 4  ...(i)

t₉ = – 8

`=>` a + 8d = – 8  ...(ii)

Subtracting (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 p^th term of this A.P. be 0

`=>` 8 + (p – 1) × (–2) = 0

`=>` 8 – 2p + 2 = o

`=>` 10 – 2p = 0

`=>` 2p = 10

`=>` p = 5

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