Can any term of A.P., 12, 17, 22, 27, ... be zero? Why?

Formula Used.

d_n = a_{n + 1} – a_n

a_n = a + (n–1)d

In the above sequence,

a = 12;

d₁ = a₂–a₁ = 17–12 = 5

d₂ = a₃–a₂ = 22–17 = 5

d₃ = a₄–a₃ = 27–22 = 5

The difference in sequence is same and comes to be (5).

For any term of A.P to be 0

a_n = a + (n–1)d = 0

a_n = a + (n–1)d = 12 + (n–1)(5)

= 12 + 5n–5

= 7 + 5n

7 + 5n = 0

5n = –7

n =

∴ The number of terms cannot be negative

Hence, the no term of A.P can be 0