Question

A king wanted to reward his advisor, a wise man of the kingdom. So he asked the Wiseman to name his own reward. The Wiseman thanked the king but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, $3$ coins for the second day, $5$ coins for the third day and so on for $30$ days. Without making calculations, find how many coins will the advisor get in that month?

Answer 1

Total coins the advisor gets at the end $=1+3+5+..................................$

We have to determine the number of coins will the advisor get in $30$ days,

The coins order is in the series of odd natural numbers,

So, the number of terms ($n$) $=30$

Then,

Sum of odd natural numbers $=n^2={30}^2=900$

Hence, the advisor gets $900$ coins in $30$ days.