Question 1

We need to find the total money after each month. We will then write a general expression.

Step 1 — Calculate monthly amounts

The student starts with ₹500. She gets ₹150 every month. Let's calculate the money at the end of each month.

At the end of the 2nd month: $= 500 + (2 \times 150)$ $= 500 + 300$

$\boxed{₹800}$

At the end of the 3rd month: $= 500 + (3 \times 150)$ $= 500 + 450$

$\boxed{₹950}$

At the end of the 4th month: $= 500 + (4 \times 150)$ $= 500 + 600$

$\boxed{₹1100}$

Step 2 — Find the linear expression

We can see a pattern in the calculations. The initial amount is ₹500. The pocket money is ₹150 per month. For $n$ months, she gets $n \times 150$.

Let $A_n$ be the amount in the $n^{\text{th}}$ month. $A_n = \text{Initial amount} + (\text{Number of months} \times \text{Pocket money})$ $A_n = 500 + (n \times 150)$ $A_n = 500 + 150n$

$\boxed{A_n = 150n + 500}$

Answer

(i) At the end of the 2nd month, she will have ₹800. (ii) At the end of the 3rd month, she will have ₹950. (iii) At the end of the 4th month, she will have ₹1100. (iv) The linear expression for the $n^{\text{th}}$ month is $A_n = 150n + 500$.