Question

On $1^{st}$ Jan $2016$, Sanika decides to save $Rs.10$, $Rs.11$ on second day, $Rs.12$ on third day. If she decides to save like this, then on ${31}^{st}$ Dec $2016$ what would be her total saving?

Answer 1

The money saved at first day is $Rs10$, atsecond day $Rs11$, at third day $Rs12$ and so on.

Since the year $2016$ is a leap year, therefore the total number of days in a leap year is $366$.

Thus, the money saved by her will form an A.P.,

$10+11+12+\cdots \left(upto31stdec\right)$

Here, $a=10$, $d=1$ and $n=366$

So, the sum of the above A.P. is,

$S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$

$=\frac{366}{2}\left[2\left(10\right)+\left(366-1\right)1\right]$

$=183[20+365]$

$=183\times 385$

$=70455$

Therefore, the total saving made by her is $70455.$