Question

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

Answer 1

Given that,

Ramkali weekly savings: $5,(5+1.75),(5+2\times 1.75)$

i.e, $5,6.75,\mathrm{8.5......}$

Her $n^{th}$ weekly savings is $Rs.20.75$

The above series is in AP, where

First term, $a=5$

Common difference, $d=6.75-5=1.75$

$n^{th}$ term, $a_n=20.75$

$n=?$

We know that the $n^{th}$ os an AP is given by

$a_n=a+(n-1)d$

$\Rightarrow 20.75=5+(n-1)1.75$

$\Rightarrow 15.75=(n-1)1.75$

$\Rightarrow (n-1)=\frac{15.75}{1.75}=\frac{1575}{175}$

$\Rightarrow (n-1)=\frac{63}{7}=9$

$\Rightarrow n=10$

Hence, her ${10}^{th}$ weekly savings will be $Rs.20.75$