Alright, lets get started.
Missing number fom the series : 9, ..... , 6561, 43046721
43046721 is square of its previous number 6561, means
![6561^2 = 43046721](https://tex.z-dn.net/?f=%206561%5E2%20%3D%2043046721%20)
It means the missing number will be square of its previous number
Means
, so missing number is 81. : Answer
Next : one number is 2 more than 3 times another. their sum is 22. find the numbers.
Suppose one number is x and second number is y
As per given equation,
......equation (1)
Their sum is 22 means,
.......equation (2)
Putting the value of x from equation1 into equation 2
![3y + 2 + y = 22](https://tex.z-dn.net/?f=%203y%20%2B%202%20%2B%20y%20%3D%2022%20)
Subtracting 2 in both sides
![4y + 2 - 2 = 22 - 2](https://tex.z-dn.net/?f=%204y%20%2B%202%20-%202%20%3D%2022%20-%202%20)
![4y = 20](https://tex.z-dn.net/?f=%204y%20%3D%2020%20)
![y = 5](https://tex.z-dn.net/?f=%20y%20%3D%205%20)
![x = 22 - y = 22 - 5 = 17](https://tex.z-dn.net/?f=%20x%20%3D%2022%20-%20y%20%3D%2022%20-%205%20%3D%2017%20)
Means numbers are 17 and 5. : Answer
Next : the missing number in the series 1, 4, 27,____, 3125 is
1 could be written as 1
4 could be written as ![2^2](https://tex.z-dn.net/?f=%202%5E2%20)
27 could be written as ![3^3](https://tex.z-dn.net/?f=%203%5E3%20)
So , next number would be ![4^4](https://tex.z-dn.net/?f=%204%5E4%20)
![4^4 = 256](https://tex.z-dn.net/?f=%204%5E4%20%3D%20256%20)
Next one is ![5^5 = 3125](https://tex.z-dn.net/?f=%205%5E5%20%3D%203125%20)
So, the missing number is 256 : Answer
Next : the next number in the series 3, 4, 6, 7, 9, 10 is
After 3,4 (5) is mising, 6, 7 (8) is missing, 9, 10 (11) will be missing
So, next number will be 12. : Answer
Next : a farmer is planting a straight row of crops with 3 feet between each plant. if 23 are planted, what is the distance between the first and last plant?
Between 2 plants, the distance is = ![3 * (2-1) = 3](https://tex.z-dn.net/?f=%203%20%2A%20%282-1%29%20%3D%203%20)
Between 3 plants, the distance is = ![3 * (3-1) = 6](https://tex.z-dn.net/?f=%203%20%2A%20%283-1%29%20%3D%206%20)
So, between 23 plants, the distance is = ![3 * (23-1) = 3 * 22 = 66](https://tex.z-dn.net/?f=%203%20%2A%20%2823-1%29%20%3D%203%20%2A%2022%20%3D%2066%20)
hene the distance between first and last plant woule be 66 feet. : Answer