Q7 of 176 Page 9

In which of the following situations does the list of numbers involved arithmetic progression, and why?

The values of an investment after 1, 2, 3, 4, ... years if after each subsequent year it increases by 5/4 times the initial investment.

Let the initial investment be I,


After one year it increases by I,


So the investment becomes, I + I


= I


At the end of 2nd year it again increase to I,


So the investment becomes, (I + I + I )


=( I + I)


= I


At the end of the 3rd year it again increases to I


So the investment becomes (I + I + I + I )


= I + I + I


= I+ I


= I


Therefore the series is:


I, I, I, I,………


Now difference between 2nd and 1st term is I – I = I


difference between 3rd and 2nd term is I I = I


Since the difference is same,


Hence the obtained series is an A.P.


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