Can any term of A.P., 201, 197, 193, ... be 5? Why?

Formula Used.

d_n = a_{n + 1} – a_n

a_n = a + (n–1)d

In the above sequence,

a = 201;

d₁ = a₂–a₁ = 197–201 = –4

d₂ = a₃–a₂ = 193–197 = –4

The difference in sequence is same and comes to be (–4).

For any term of A.P to be 5

a_n = a + (n–1)d = 5

a_n = a + (n–1)d = 201 + (n–1)(–4)

5 = 201–4n + 4

5 = 205–4n

–4n = –205 + 5

n = = 50

∴ The 50^th term of A.P is 5