Question

1) Examine that the sequence obtained from the following situation will be in the form of an A.P or not.The amount of money in the account every year when Rs 100 is

deposited at compound intrest 4 % per Annum .​

Answer 1

Solution:

(Initial Year)

Principal = Rs. 100

Rate = 4% per annum

The amount in the beginning is Rs. 100

(First Year)

Compound Interest rate amount at end of first year ,

$A = P(1 + \frac{r}{n})^{n}$

$A = 100(1 + \frac{4}{1 * 100})^{1}\\A = 100(1 + 0.04)\\A = 100 * 1.04\\A = 104$

(Second Year)

New Principal = Rs. 104

Compound Interest rate amount at end of second year ,

$A = P(1 + \frac{r}{n})^{n}\\A = 104(1 + \frac{4}{1 * 100})^{1}\\A = 104(1 + 0.04)\\A = 104 * 1.04\\A = 108.16$

(Third Year)

New Principal = Rs. 108.16

Compound Interest rate amount at end of second year ,

$A = P(1 + \frac{r}{n})^{n}\\A = 108.16(1 + \frac{4}{1 * 100})^{1}\\A = 108.16(1 + 0.04)\\A = 108.16 * 1.04\\A = 112.4864$

and so on.

So, the sequence is going like 100 , 104 , 108.16.....................

An AP(Arithmetic Progression) is having a sequence of numbers which is having a constant difference from the previous quantity.

Difference means second minus the first.

Difference between =>  

104 - 100 = 4  

108.16 - 104 = 4.16   and so on.

So, the difference is varying.

Therefore, it is not an AP.