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Does the list of numbers involved in following situation make an arithmetic progression, and why?The taxi fare after each km when the fare is (Rs15) for the first km and (Rs8)for each additional km.

Question

Does the list of numbers involved in following situation make an arithmetic progression, and why?The taxi fare after each km when the fare is \(Rs15\) for the first km and \(Rs8\)for each additional km.  

Answer

\(8\) yes, it is an \(AP\)
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Solution

According to question, the fare for journey of first km i.e., \(1 \text{km}\) is\(Rs15\)and next \(2\text{km},3\text{km},4\text{km}\dots \)are respectively\(Rs(15+8),Rs(15+2\times 8),\)\(Rs(15+3\times 8),\dots \)so on
i.e. \(15,23,31,39..\)
As difference of two consecutive terms is 8 \([\because 23-15=31-23=39-31=8]\)
So, it is an A.P.
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