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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

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Answer:

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.

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