The sum of 6 consecutive integers is 393. What is the third number In this sequence?

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Answer 1 · 2016-12-10T15:06:29

65

Let's define the first integer as #x#. Then the next five consecutive integers would be:

#x + 1#, #x + 2#, #x + 3#, #x + 4# and #x + 5#.

The sum of these six integers is 393 so we can write:

#x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 393#

#6x + 1 + 2 + 3 + 4 + 5 = 393#

#6x + 15 = 393#

#6x + 15 - 15 = 393 - 15#

#6x + 0 = 378#

#(6x)/6 = 378/6#

#x = 63#

Because the first integer is 63 then the third would be #x + 2# or #63 + 2 = 65#