Design and write a program to calculate the sum of integers in a given range. The formula for calculating this sum is: sum = (n/2) (2xa+(n-1)d) where n is the number of integers to be added, a is the first number, d is the difference between each number. Your program should get these values from the user and display the results.

Matlab question: use switch and anythe lottery game matches three different integer numbers between 1 and 10. winning depends on how many matching numbers are provided by a player. the player provides three different integers between 1 and 10.if there is a match of all 3 numbers, the winning $ 1000.if there is a match with 2 numbers, the winning $ 10.if there is a match of all with 1 numbers, the winning $ 1.with no match, the winning is $0.write a function lottery3 that checks three numbers provided by a player and determine the winning amount. if the user mistakenly enters same number twice/thrice and if that number matches one of the winning numbers, the code should count that number only once and display correct result. the player doesn’t have to guess the order of numbers.the input to the function lottery3 can have up to two input arguments. the first input argument is a row array numbers with 3 numbers. if the second argument input testcode is present, and is a row vector of 3 values, the function lottery3 uses the code in testcode as the three winning numbers (the test must be three different integer numbers between 1 and 10), else three different numbers will be automatically generated by testcode.the ouput should return the variable winnings and the three winning numbers in the row array winnumbers.hint: make use of the internal function any.restriction: the function must use switch-case statements to determine the winning.example #1: winning = lottery3( [1,2,1],[1,2,3])produceswinning =10example #2: [winning,winnumbers] = lottery3( [1,2,3])produceswinning =3winnumbers =8 5 3

)a grad student comes up with the following algorithm to sort an array a[1..n] that works by first sorting the first 2/3rds of the array, then sorting the last 2/3rds of the (resulting) array, and finally sorting the first 2/3rds of the new array. 1: function g-sort(a, n) . takes as input an array of n numbers, a[1..n] 2: g-sort-recurse(a, 1, n) 3: end function 4: function g-sort-recurse(a, `, u) 5: if u ⒠` ≤ 0 then 6: return . 1 or fewer elements already sorted 7: else if u ⒠` = 1 then . 2 elements 8: if a[u] < a[`] then . swap values 9: temp ↠a[u] 10: a[u] ↠a[`] 11: a[`] ↠temp 12: end if 13: else . 3 or more elements 14: size ↠u ⒠` + 1 15: twothirds ↠d(2 ◠size)/3e 16: g-sort-recurse(a, `, ` + twothirds ⒠1) 17: g-sort-recurse(a, u ⒠twothirds + 1, u) 18: g-sort-recurse(a, `, ` + twothirds ⒠1) 19: end if 20: end function first (5 pts), prove that the algorithm correctly sorts the numbers in the array (in increasing order). after showing that it correctly sorts 1 and 2 element intervals, you may make the (incorrect) assumption that the number of elements being passed to g-sort-recurse is always a multiple of 3 to simplify the notation (and drop the floors/ceilings).

What role do chromosomes play in inheritance?