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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.

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Solution

No, the given statement is not true because the total fare (in ₹) after each km is :
15,(15+8), (15+2×8), (15+3×8), ...
i.e 15,23,31,39,
Let t1=15, t2=23, t3=31 and t4=39
Now, t2t1=2315=8
t3t2=3123=8
t4t3=3931=8
Since, the difference between the consecutive terms is same, it is an AP.

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