Question 129

A king wanted to reward his advisor, a wiseman of the kingdom. So, he asked the wiseman to name his own reward. The wise man 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?

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Solution

Let the advisor get $x$ coins in that month.
According to the question, advisor gets coins up to 30 days as the pattern.
$x$ = 1 + 3 + 5 + ...
Here, n = 30
We know that, sum of first n odd natural numbers $= n^{2} = (30)^{2} = 30 \times 30 = 900$
Hence, the advisor get 900 coins in that month.

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Addition of Odd Numbers

Standard VIII Mathematics

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Let the advisor get x coins in that month. According to the question, advisor gets coins up to 30 days as the pattern. x = 1 + 3 + 5 + ... Here, n = 30 We know that, sum of first n odd natural numbers =n2=(30)2=30×30=900 Hence, the advisor get 900 coins in that month.

Let the advisor get $x$ coins in that month.
According to the question, advisor gets coins up to 30 days as the pattern.
$x$ = 1 + 3 + 5 + ...
Here, n = 30
We know that, sum of first n odd natural numbers $= n^{2} = (30)^{2} = 30 \times 30 = 900$
Hence, the advisor get 900 coins in that month.