Question

In the following situations, does the list of numbers involved make an arithmetic progression, and why ? The taxi fare after each km when the fare is $\mathrm{Rs}15$ for the first km and $\mathrm{Rs}8$ for each additional $\mathrm{km}$.

Answer 1

Analyze the situation.

The given conditions can be expressed as,

Taxi fare for $1\mathrm{km}$$=\mathrm{Rs}15$

Taxi fare for first $2\mathrm{kms}=\mathrm{Rs}23$

Taxi fare for first $3\mathrm{kms}=\mathrm{Rs}31$

Taxi fare for first $4\mathrm{kms}=\mathrm{Rs}39$

Let's make a series

$15,23,31,39....;...$

We know that A.P. is a sequence of numbers in which the difference between any two consecutive numbers is a constant value. Here every consecutive term can be derived by adding $8$ to the previous term.

$23-15=31-23=...=8$

Hence given situation forms an A.P. with first term of $15$ and common difference $8$.