Hey! my girl needs some on her math and i forgot how to do integers,
1) in a list of consecutive integers, each integer is one greater than the preceding integer. for example, 8, 9, and 10 are three consecutive integers.
also, -7, -6, -5, and -4 are four consecutive integers.
a. start with -2. write a list of four consecutive integers.
b. start with n. write expressions for four consecutive integers.
c. write expressions for three consecutive integers if the middle integer is n.
d. write and simplify an expression for the sum of two consecutive integers.
2. a. use your expression from excercise 1d. show that the sum of two consecutive integers is always odd.
b. show that the sum of three consecutive integers is always divisible by 3.
c. is the sum of four consecutive integers divisible by 4? explain.
d. is the sum of five consecutive integers divisible by 5? explain.
e. take it further. for what whole numbers k is the sum of k consecutive integers always divisible by k?
3. if n is an integer, then the expression n(n+1) represents the product of two consecutive integers.
a. explain how you know that the product of two consecutive integers is an even number.
b. is the product of three consecutive integers divisible by three? explain.
c. is the product of four consecutive integers divisible by 4? explain.
d. is the product of five consecutive integers divisible by 5? explain.