Write and simplify an expression to represent the sum of three consecutive odd integers.?
you could write x + x+2 + x+4, but what if x is even?
To make sure we have only odd numbers use
2x+1 + 2x+3 + 2x+5 = 6x+9 = 3(2x+3)
so the sum of 3 consecutive odd numbers is just 3 times the middle one. You can see this more easily if you let the numbers be
x-2 + x + x+2 = 3x
In fact, the sum of any three consecutive terms of an arithmetic sequence is just 3 times the middle term.
This really helped me. Thanks!
Let's represent the first odd integer as "x". Since the integers are consecutive, the next odd integer would be "x + 2" and the one after that would be "x + 4".
To find the sum of these three integers, we add them together:
x + (x + 2) + (x + 4)
Simplifying the expression, we combine like terms:
3x + 6
So, the simplified expression to represent the sum of three consecutive odd integers is 3x + 6.
To represent the sum of three consecutive odd integers, we can let the first odd integer be x. Since the integers are consecutive, the second odd integer would be x + 2, and the third odd integer would be x + 4.
To find the sum of these three integers, we add them together:
x + (x + 2) + (x + 4)
To simplify the expression, we combine the like terms:
x + x + 2 + x + 4
This simplifies to:
3x + 6
So the expression that represents the sum of three consecutive odd integers is 3x + 6.