Answer:

Let the series be 7, A₁, A₂, A₃, …….., A_n, 71

Total terms in AP are n + 2

71 is the (n + 2)th term

By using the formula,

A_n = a + (n – 1)d

A_n = 71, n = 6

A₆ = a + (6 – 1)d

a + 5d = 27 (5^th term)

d = 4

71 = (n + 2)th term

71 = a + (n + 2 – 1)d

71 = 7 + n(4)

n = 15

∴ There are 15 terms in AP