Question

Question 6
The taxi fare after each km, when the fare is ₹ 15 for the first km and ₹ 8 for each additional km, does not form an AP as the total fare (in ₹) after each km is 15, 8, 8, 8, … Is the statement true? Give reasons.

Answer 1

No, the given statement is not true because the total fare (in ₹) after each km is :
$15,(15+8),(15+2\times 8),(15+3\times 8),...$
$i.e15,23,31,39,\cdots$
$Let{t}_1=15,t_2=23,t_3=31and{t}_4=39$
$Now,t_2-t_1=23-15=8$
$t_3-t_2=31-23=8$
$t_4-t_3=39-31=8$
Since, the difference between the consecutive terms is same, it is an AP.