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Question

# Verify if the sequence of numbers formed will form an AP or not. 1- The amount of air present in the cylinder when a vacuum pump removes each time 1/4 of air remaining in the cylinder. 2- Divya deposited ₹1000 at compound interest at the rate of 10% per annum. The amount at the end of first year, second year, third year,....., and so on.

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Solution

## 1) Let us assume, initial quantity of air = V Therefore, quantity removed in the first step = V × 14 Quantity remaining after the first step = V−V4 = 3V4 Quantity removed in the second step = 3V4 × 14 = 3V16 Quantity remaining after the second step = 3V4 - 3V16 = 9V16 Quantity remaining after each step follows the trend: V,3V4,9V16,... Here each subsequent term is not obtained by adding a fixed number to the previous term. Hence, it is not an AP. 2) First year principal = A0 = Rs 1000 r = 10% Time period ( t ) = 1 yr Amount at the end of First year( A1) = 1000 ( 1 + 10 / 100 ) = 1000 × 110 / 100 A1 = Rs 1100 second year principal = A1 = Rs 1100 r = 10 % Time period ( t ) = 1 yr Amount at the end of Second year( A2) = 1100 ( 1 + 10 / 100 ) = 1100 × 110 /100 A2 = Rs 1210 third year principal = A2 = Rs 1210 r = 10 % Time period ( t ) = 1 year A3 = 1210 ( 1 + 10 /100 ) = 1210 × 110 / 100 A3 =Rs 1331 Therefore, First year , second year ,third year ending Amounts are 1100 , 1210 , 1331 ,... a2 - a1 = 1210 - 1100 = 110 a3 - a2 = 1331 - 1210 = 121 Therefore , a2 - a1 is not equal to ( a3 - a2 ) This is not an A.P I hope this helps you.

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