(Q23).In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?

(i) The amount of money in the account every year, when Rs. 10000 is deposited at compound interest at 8 % per annum.

Amount deposited initially = P = Rs. 10,000

Rate of interest = R = 8% p.a [at C.I.]

∴ A=P(1+
R
100
 )n

Years 1 2 3 .....
Amount
10000 ( 1 +
8
100
 ) =
10000 ( 1 +
8
100
 )2 =
10000 ( 1 +
8
100
 )3 =
.....

The terms , , , ……. , a2 – a1 =

Here, a = 10,000 , a3 – a2 =

But, a2 – a1 ≠ a3 – a2 ≠ a4 – a3 , a4 – a3 =

∴ The given situation doesn’t represent an A.P.