Find the nth term of the following A.P.'s:

1000, 900, 800, ...

Formula Used.

d_n = a_{n + 1} – a_n

a_n = a + (n–1)d

In the above sequence,

a = 1000;

d₁ = a₂–a₁ = 900–1000 = –100

d₂ = a₃–a₂ = 800–900 = –100

The difference in sequence is same and comes to be (–100).

∴ The above sequence is A.P

The n^th term of A.P is a_n = a + (n–1)d

a_n = a + (n–1)d = 1000 + (n–1)(–100)

= 1000–100n + 100

= 1100–100n