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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