Classrooms on one side of the science building are all numbered with consecutive odd integers. If the first room, the room with the smallest classroom number, on this side of the building is numbered k, write an expression in k for the sum of the first five classroom numbers in a row. Then simplify this expression. The sum of the first five classroom numbers in a row is

The sum of the first five classroom numbers in a row is 5k + 20

Step-by-step explanation:

Since the smallest classroom number on the side of the building is numbered k and each consecutive odd integer is separated by a difference of  

2.

Therefore:  

k is the first class room.

k +  2  is the second class room.

k +  4  is the third class room.

k + 6 is the third class room.

k + 8 is the fifth class room.

The sum of the five consecutive class rooms are given as:

k + (k + 2) + (k + 4) + (k + 6) + (k + 8)

collecting alike terms we get

=  k + k + k + k + k + 2 + 4 + 6 + 8

= 5k + 20

Therefore, The sum of the first five classroom numbers in a row is 5k + 20.

correct answers below: