Question

On 1st 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

On 1^st Jan 2016, Sanika saved Rs 10.
Next day Rs 11.
Third day Rs 12.

Her total savings = Rs (10 + 11 + 12 + ... + till 31^st Dec)

Here,
a = 10
d = 1
n = 366 (since 2016 is a leap year)

Now,
$$\begin{gathered} S_n=\frac{n}{2}\left(2a+\left(n-1\right)d\right) \\ \Rightarrow S_{366}=\frac{366}{2}\left(2\left(10\right)+\left(366-1\right)1\right) \\ =183\left(20+365\right) \\ =70455 \end{gathered}$$

Hence, her total savings would be Rs 70455.