Question

ARITHMETIC PROGRESSIONS

explain whether the situation is in ap with calculations:
Divya deposited ₹1000 at compound interest at the rate of 10% per annum the amount at the end of the first year, second year, third year....and so on

Answer 1

Given  : Divya deposited Rs.1000 at compound interest at the rate of 10 % per annum.

We know formula for compound interest  :

Amount  = P1 + r100t , Here

P  =  Principle amount  = Rs . 1000

r = Rate of interest  =  10%

And

t  =  Time in years  .

So,
Amount at the end of first year  = 10001 + 101001 = 10001 + 110 = 1000 × 1110 = Rs. 1100
And
Amount at the end of second year  = 10001 + 101002 = 10001 + 1102 = 1000 × 1110 × 1110= Rs. 1210
And
Amount at the end of third year  = 10001 + 101003 = 10001 + 1103 = 1000 × 1110 × 1110× 1110= Rs. 1331

So,

1100 , 1210 , 1331 , .. 

1210 - 1100 = 110

1331 - 1210 = 121

So,

110 ≠ 121

So,


1100 , 1210 , 1331 , ..   Not in A.P.

Answer 2

This is not in AP, as the common difference compound interest are not same .