Question

A king wanted to reward his adviser,a wise man of the kingdom.so he asked the wiseman to name his own reward.the wiseman thanked the king but said he would ask only for some gold coins each day for a month.the coins were to be counted out in a pattern of 1 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? mention the property used to find the answer.

(square an square roots)

Answer 1

900 coins

Explanation:

The Wiseman demands 1 gold coin for the 1st day, then 3 gold coins for the 2nd day, then 5 gold coins for the 3rd day and it continues for 30 days in this pattern.

Therefore, the total number of gold coins that he gets will be,

1+ 3+ 5+ ..... up to 30 terms.

This is an A.P. series with the first term(a) 1 and a common difference(d) 2 and the number of terms(n) 30.

Hence, the sum of the A.P. series is given by
`(n)/(2) [2a+(n-1)d]`

=
`(30)/(2) [2*1+(30-1)*2]`

= 900 coins (Answer)