Question

In the following situation, the sequence of numbers formed will form an A.P.?

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.

Answer 1

Given: Divya deposited P = ₹ 1000 at compound interest r = 10% per annum.

Step-wise calculation:

1. General formula for the amount at the end of n years:

`A_n = P(1 + r/100)^n`

2. Here A_n = 1000(1.10)ⁿ. So

A₁ = 1000 × 1.10

= ₹ 1100

A₂ = 1000 × (1.10)²

= ₹ 1210

A₃ = 1000 × (1.10)³

= ₹ 1331

3. Check successive differences:

A₂ – A₁ = 1210 – 1100

= ₹ 110

A₃ – A₂ = 1331 – 1210

= ₹ 121

Since 110 ≠ 121, the difference between consecutive terms is not constant.

The sequence of amounts 1100, 1210, 1331, ... is a geometric progression (each term multiplied by 1.10) and does not form an arithmetic progression (A.P.).