Answer:
Total weight of the wheat placed on 45th square will be = ![1.26\times 10^{6}tons](https://tex.z-dn.net/?f=1.26%5Ctimes%2010%5E%7B6%7Dtons)
Step-by-step explanation:
King rewarded the inventor of chess by giving grain of wheat on every square of the chess board. He places one grain of wheat on first square, 2 on second, 4 on 3rd, 8 on 4th and so on.
In fact he places grains of wheat in a progression S = 1, 2, 4, 8, 16.........n terms where value of n is 64.
We can rewrite the progression as S = 2°, 2, 2², 2³,.........n terms (n = 64)
In a geometric progression we know the nth term = ![a(r^{n-1})](https://tex.z-dn.net/?f=a%28r%5E%7Bn-1%7D%29)
where a = first term of the series, r = common ratio, n = number of terms
Now we have to calculate the weight of all wheat placed on 45th square.
So we will put the values in the given formula 45th term =
=
=![1.76\times 10^{13}](https://tex.z-dn.net/?f=1.76%5Ctimes%2010%5E%7B13%7D)
Then the weight of wheat will be =
=![1.26\times 10^{6}tons](https://tex.z-dn.net/?f=1.26%5Ctimes%2010%5E%7B6%7Dtons)