Question

Aditi required $₹2500$ after $12$ weeks to send her daughter to school. She saved $₹100$ in the first week and increased her weekly savings by $₹20$ every week. Find whether she will be able to send here daughter after $12$ weeks.

Answer 1

Step 1: Defining the A.P.

According to the question, Aditi started saving with Rs.100 in the first week and gradually increased her savings by Rs.20 every week

Therefore, to achieve the target of Rs.2500 at the end of 12 weeks.

So, we need to determine the sum of the total savings.

Now, Arithmetic Progression (A.P.) of the savings will be $100,120,140,\dots \dots$

Step 2: Calculate the total savings.

If you know the first term and the total number of terms. The sum of Arithmetic Progression (A.P.) is calculated as follows:

$\begin{array}{rcl}{S}_n& =& \frac{n}{2}\left(2a+\left(n-1\right)d\right)\end{array}$

Where $a$ is the first term, $n$ is the number of terms, $d$ is a common difference, and $S_n$ is the sum of the series.

In our Arithmetic Progression (A.P.), $a=100$, $d=20$, and $n=12$,, then

$\begin{array}{rcl}{S}_n& =& \frac{n}{2}\left(2a+\left(n-1\right)d\right)\\ & =& \frac{12}{2}\left(200+11\times 20\right)\\ & =& 6\left(420\right)\\ & =& ₹2520\end{array}$

Therefore, Aditi's total savings is Rs 2520 which is clearly more than Rs 2500, and she will be able to send her daughter to school.

Final answer:

Hence, she will be able to send her daughter to school.