Question

the third term of A.P is p and the fourth term is q. show that nth term of an A.P is tn = 4p - 3q + ( q - p) n​

Answer 1

So we have,

a + 2d = p → (1)

a + 3d = q → (2)

Well,

(2) - (1) => d = q - p

(1) × 4 => 4a + 8d = 4p → (3)

(2) × 3 => 3a + 9d = 3q → (4)

Then,

(3) - (4) => a - d = 4p - 3q

Now,

t_n = a + (n - 1)d

t_n = a + dn - d

t_n = a - d + dn

t_n = 4p - 3q + (q - p)n

Done!