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 $km$ is $15, 8, 8, 8, \ldots$. Is the statement true? Give reasons.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(B) No,the statement is false. The total fare (in $Rs.$) after each $km$ is calculated as follows:
For $1$ $km$: $15$
For $2$ $km$: $15 + 8 = 23$
For $3$ $km$: $15 + 2 \times 8 = 31$
For $4$ $km$: $15 + 3 \times 8 = 39$
Thus,the sequence of total fares is $15, 23, 31, 39, \ldots$.
Let $t_1 = 15, t_2 = 23, t_3 = 31, t_4 = 39$.
Now,calculating the common difference:
$t_2 - t_1 = 23 - 15 = 8$
$t_3 - t_2 = 31 - 23 = 8$
$t_4 - t_3 = 39 - 31 = 8$
Since the difference between consecutive terms is constant (common difference $d = 8$),the sequence forms an Arithmetic Progression $(AP)$.

Explore More

Similar Questions

The $n^{th}$ term of an $A.P.$ is given by $T_n = 3n - 1$. For this $A.P.$,the common difference $d = \ldots$

The measures of all the four angles of a quadrilateral form an $A.P.$. If the common difference is $10^{\circ}$,find the measures of all the angles.

Difficult
View Solution

Write the first three terms of the $APs$ when $a$ and $d$ are as given below:
$a = \sqrt{2}, d = \frac{1}{\sqrt{2}}$

Two APs have the same common difference. The first term of one $AP$ is $2$ and that of the other is $7$. The difference between their $10^{\text{th}}$ terms is the same as the difference between their $21^{\text{st}}$ terms,which is the same as the difference between any two corresponding terms. Why?

Difficult
View Solution

Find the $12^{\text{th}}$ term from the end of the $AP: -2, -4, -6, \ldots, -100$.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo