In which of the following situations does the list of numbers involved

1.	In which of the following situations does the list of numbers involved arithmetic progression, and why?The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.
Answer» Taxi fare for 1km = 15 According to question, Rs. 8 for each additional km ⇒ Taxi fare for 2km = 15 + 8 =23 and Taxi fare for 3km = 23 + 8 =31 Therefore, series is 15, 23, 31 ,… Difference between 2^nd and 1^st term = 23 – 15 = 8 Difference between 3^rd and 2^nd term = 31 – 23 = 8 Since, difference is same. Hence, the taxi fare after each km form an AP with the first term, a = Rs. 15 and common difference, d = Rs. 8

In which of the following situations does the list of numbers involved arithmetic progression, and why?The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

Answer»

Taxi fare for 1km = 15

According to question, Rs. 8 for each additional km

⇒ Taxi fare for 2km = 15 + 8 =23

and Taxi fare for 3km = 23 + 8 =31

Therefore, series is

15, 23, 31 ,…

Difference between 2^nd and 1^st term = 23 – 15 = 8

Difference between 3^rd and 2^nd term = 31 – 23 = 8

Since, difference is same.

Hence, the taxi fare after each km form an AP with the first term, a = Rs. 15 and common difference, d = Rs. 8