How do you find three consecutive odd integers?

1 Answer
Jun 10, 2015

Answer:

Three consecutive odd integers are always of the form #(2k+1)#, #(2k+3)# and #(2k+5)# for some integer #k#.

Explanation:

Every odd integer can be expressed in the form #2k+1# for some integer #k#.

Given an odd integer #2k+1#, the next odd integer is #(2k+1)+2 = 2k+3# and the next after that is #2k+5#.

If you want to find three consecutive odd integers to satisfy some property then you can substitute these expressions into the condition and solve for #k#.

For example, to find three consecutive odd integers whose sum is #189# you can write:

#189 = (2k+1) + (2k+3) + (2k+5) = 6k+9#

Subtract #9# from both sides to get:

#180 = 6k#

Divide both sides by #6# to get #k = 30#.

Then our three odd integers are

#(2k + 1) = 61#, #(2k+3) = 63# and #(2k+5) = 65#