Question

Ramkali saved $₹5$ in the first week of a year and then increased her weekly saving by $₹1.75$. If in the $\mathrm{nth}$ week, her weekly savings become $₹20.75$, find $\mathrm{n}$.

Answer 1

Step 1: Identify the problem based on the given statement

Given that

Ramkali saved $₹5$ in the first week and then increased saving each week by $₹1.75$.

We need to find out the week when the savings becomes $₹20.75$

So, its a A.P problem

First-term $\left(a\right)=5$

and common difference $\left(d\right)=1.75$

let nth term is $₹20.75$

$\Rightarrow a_n=20.75$

Step 2: Use general term formula and find the value of $\mathrm{n}$

We know that

${\mathrm{a}}_{\mathrm{n}}=\mathrm{a}+(\mathrm{n}-1)\mathrm{d}$

$$\begin{gathered} \Rightarrow 20.75=5+(n-1)\times 1.75 \\ \Rightarrow 15.75=(n-1)\times 1.75 \\ \Rightarrow (n-1)=\frac{15.75}{1.75}=\frac{1575}{175}=9 \\ \Rightarrow n-1=9 \\ \Rightarrow n=10 \end{gathered}$$

Hence, in the $10th$ week, her weekly savings become $₹20.75$,