For this exercise, we are asked to find the sum of three consecutive odd integers given that the first one is 2n+1. Since odd integers are each two more than the previous one, we can obtain the three consecutive odd integers by adding 2 to the previous one.
First Odd Integer: ( 2n+1)
Second Odd Integer: ( 2n+1) + 2 = ( 2n+3)
Third Odd Integer: ( 2n+3) + 2 = (2n+5)
Now, we can add our three expressions together to find a polynomial to represent the sum.
( 2n+1)+( 2n+3)+(2n+5)= 6n+9
Extra
Consecutive Odd Integers
Sometimes it helps to write out a couple of examples to see how each odd number relates to the previous one. Let's let n=4 to find a random odd number to start with, 2n+1=2(4)+1. We can start our table with 9. We know the next two consecutive odd numbers are 11 and 13.
