Question

The taxi fare after each km, when the fare is Rs 15 for the first km and Rs 8 for each additional km, does not form an AP as the total fare (in Rs) after each km is 15, 8, 8, 8, … . Is the statement true? Give reasons.

Answer 1

No, because the total fare after each km is

15, 15 + 8, 15 + 8(2), 15 + 8(3) …….

15, 23, 31, 39….

a₁ = 15, a₂ = 23, a₃ = 31 and a₄ = 39

a₂ - a₁ = 23 - 15 = 8

a₃ - a₂ = 31 - 23 = 8

a₄ - a₃ = 39 - 31 = 8

Since, all the successive terms of the given list have same difference i.e., common difference = 8.

Hence, the total fare after each km forms an AP.