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State if the following is true or false.

In following situation, the list of numbers involved arithmetic progression.

The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

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True

False

answer is A.

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Detailed Solution

Given that,
The taxi fare for

1

km is Rs

15.

The increment is Rs

8 for each additional km.
Now, the fare for the second km will be,

a 2 = 15 + 8 ⇒ a 2 = 23

Similarly, te fare of the third km will be,

a 3 = 23 + 8 ⇒ a 3 = 31

So, the series will be

15, 23, 31, ...

.
Now, the common difference will be,

a 2 − a 1 = 23 − 15 ⇒ a 2 − a 1 = 8

a 3 − a 2 = 31 − 23 ⇒ a 3 − a 2 = 8

Hence, the taxi fare after each km form A.P. with common difference of

8

and first term 15.
The taxi fare after each km forms A.P.
Therefore, the statement is true.
Hence, option 1 is correct.

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