In which of the following situations, do the lists of numbers involved form an $ A P $ ? Give reasons for your answers.
The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is Rs 250 , and it increases by Rs 50 for the next higher class.
Given:
The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is Rs 250 , and it increases by Rs 50 for the next higher class.
To do:
We have to check whether the list of numbers involved in the given situation forms an \( A P \).
Solution:
The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is Rs 250 , and it increases by Rs 50 for the next higher class.
This implies, the sequence formed(in Rs.) is $250, (250+50), (250+50+50), .......$
The sequence is $250, 300, 350, .......$
In the given sequence,
$a_1=250, a_2=300, a_3=350$
$a_2-a_1=300-250=50$
$a_3-a_2=350-300=50$
Here,
$a_3-a_2=a_2-a_1$
Therefore,
The list of numbers involved in the given situation forms an \( A P \).
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