# 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.

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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 $A P$.

Updated on 10-Oct-2022 13:27:27