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# 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.

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.

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