In which of the following situations, do the lists of numbers involved form an \( A P \) ? Give reasons for your answers.
The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of \( 10 \% \) per annum.

Given:

The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of \( 10 \% \) per annum.

To do:

We have to check whether  the list of numbers involved in the given situation forms an \( A P \).

Solution:

We know that,

Simple interest $=\frac{\text { Principal } \times \text { Rate } \times \text { Time }}{100}$

$=\frac{1000 \times 10 \times 1}{100}$

$=100$

This implies,

The amount of money in the account of Varun at the end of each year(in Rs.) is,

$1000, (1000+100 \times 1),(1000+100 \times 2),(1000+100 \times 3), \ldots $

The sequence formed is,

$1000,1100,1200,1300, \ldots $

In the given sequence,

$a_1=1000, a_2=1100, a_3=1200$

$a_2-a_1=1100-1000=100$ 

$a_3-a_2=1200-1100=100$

Here,

$a_3-a_2=a_2-a_1$

Therefore,

The list of numbers involved in the given situation forms an \( A P \).

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Updated on: 10-Oct-2022

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