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

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Given:

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 $\mathrm{km}$ is $15,8,8,8, \ldots$

To do:

We have to find whether the given statement is true.

Solution:

Let

$a_1 = Rs.\ 15$

This implies,

$a_2 = Rs.\ 15 + Rs.\ 8 = Rs.\ 23$

$a_3 = Rs.\ 23 + Rs.\ 8 = Rs.\ 31$

Now, the list of fares is $Rs.\ 15, Rs.\ 23, Rs.\ 31$

$a_2 - a_1 = Rs.\ 23 - Rs.\ 15$

$= Rs.\ 8$

$a_3 - a_2 = Rs.\ 31 - Rs.\ 23$

$= Rs.\ 8$

Here,

$a_2 - a_1 = a_3 - a_2$

Therefore, the given list of fares forms an A.P. and the given statement is false.

Updated on 10-Oct-2022 13:27:27

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