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.

Options

• True

• False

Answer 1

This statement is False.

Reasons:

Because the total fare (in ?) after each km is

15,(15 + 8), (15 + 2 × 8), (15 + 3 × 8),... = 15, 23, 31, 39,...

Let t₁ = 15, t₂ = 23, t₃ = 31 and t₄ = 39

Now, t₂ – t₁ = 23 – 15 = 8

t₃ – t₂ = 31 – 23 = 8

t₄ – t₃ = 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 form an AP.