Question

Neela saves in a ‘Mahila Bachat Gat’ Rs.5 on the first day Rs.7 on the second day Rs.9 on the third day and so on. What will be her savings in the month of August?

Answer 1

Hint: Here, we will get a sequence of the form \[5,7,9,\ldots \] which forms an arithmetic progression. To calculate the savings we have to find the sum of the terms. Hence, we have to apply the formula:
${{S}_{n}}=\dfrac{n}{2}\left[ 2a+(n-1)d \right]$. Here ‘n ‘is the number of days in August, i.e. 31 days.

Complete step-by-step answer:
Here, given that Neela saves in a Mahila Bachat Gat Rs.5 on the first day, Rs.7 on the second day, Rs.9 on the third day and so on.
Here, we have to calculate Neela’s savings in the month of August.
As per the given data we will get a sequence of the form \[5,7,9,\ldots \] which forms an arithmetic progression.
 Here, the first day saving is taken as, ${{a}_{{}}}=5$
Second day saving is taken as, ${{a}_{1}}=5$.
The difference in the saving is taken as $d$,
$\begin{align}
  & \text{ }d={{a}_{1}}-a \\
 & d=7-5 \\
 & d=2 \\
\end{align}$
Here $n$ is the number of days. We know that there are 31 days in August. Therefore,
$n=31$
So, to calculate the savings in the month of August we have to consider the formula:
$\begin{align}
  & {{S}_{n}}=\dfrac{n}{2}\left[ 2a+(n-1)d \right] \\
 & \Rightarrow {{S}_{n}}=\dfrac{31}{2}\left[ 2\times 5+(31-1)2 \right] \\
 & \Rightarrow {{S}_{n}}=\dfrac{31}{2}\left[ 2\times 5+(31-1)2 \right] \\
 & \Rightarrow {{S}_{n}}=\dfrac{31}{2}\left[ 10+30\times 2 \right] \\
 & \Rightarrow {{S}_{n}}=\dfrac{31}{2}\left[ 10+60 \right] \\
 & \Rightarrow {{S}_{n}}=\dfrac{31}{2}\times 70 \\
\end{align}$
Next, by cancellation we obtain:
$\begin{align}
  & {{S}_{n}}=31\times 35 \\
 & {{S}_{n}}=1085 \\
\end{align}$
 Here, we got the sum as
${{S}_{n}}=1085$
 Therefore, the savings in the month of August is Rs.1,085

Note: Here, you can calculate sum, ${{S}_{n}}$ using another formula, i.e. ${{S}_{n}}=\dfrac{n}{2}\left( a+{{a}_{n}} \right)$ where ${{a}_{n}}$ is the n^th term, and you can find ${{a}_{n}}={{a}_{31}}=5+(31-1)\times 2$. Here, the month is given as August, therefore we are taking n as 31. Hence, depending upon month n changes.