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

50, 100, 150, 200, ...

Formula Used.

d_n = a_{n + 1} – a_n

a_n = a + (n–1)d

In the above sequence,

a = 50;

d₁ = a₂–a₁ = 100–50 = 50

d₂ = a₃–a₂ = 150–100 = 50

d₃ = a₄–a₃ = 200–150 = 50

The difference in sequence is same and comes to be 50.

∴ 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 = 50 + (n–1)(50)

= 50 + 50n–50

= 50n