Rupees 820 is nvested at the rate of 8 percent simple nterest in abank .

a) find the interest after 1 year,2year,3year

b)is the sequence of interest an arithmatic sequence ?

c) compute the interest after 23 year .

Principle amount P = 820

Rate of interest

*r*= 8%

And

We know Simple interest = $\frac{P\times r\times t}{100}$

So,

a ) Interest after 1 year = $\frac{820\times 8\times 1}{100}=\frac{6560}{100}$ = 65.60

And

Interest after 2 year = $\frac{820\times 8\times 2}{100}=\frac{13120}{100}$ = 131.20

And

And

Interest after 3 year = $\frac{820\times 8\times 3}{100}=\frac{19680}{100}$ = 196.80

b ) Now we check that these interest are in A.P. or not , as we know common difference of A.P. always equal , so

131.20 - 65.60 = 196.80 - 131.20

65.60 = 65.60 ( Satisfied )

**So, we can say that sequence of interest are in arithmetic sequence .**

C ) we know Common difference d = 65.60

And

first term = 65.60 ( interest after 1 year )

And

Number of terms n = 23

And

we know formula for n

^{th}term in A.P. , As:

T

_{n}= a + ( n - 1 ) d , So

T

_{23}= 65.60 + ( 23 - 1 ) 65.60

T

_{23}= 65.60 +22$\times $ 65.60

T

_{23}= 65.60 + 1443.2

T

_{23}= 1508.80

So,

**Interest after 23 year = Rs 1508.80 ( Ans )**

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