Let's set the first even number to #n#. Since we have #5# consecutive numbers, the second should be #n + 2#, the third is #n + 4#, fourth is #n + 6#, and finally fifth is #n + 8#. We know that they add up to #310#:
#n + (n + 2) + (n + 4) + (n + 6) + (n + 8) = 310#
Let's simplify, adding up like terms (add up all the #n#s, and add up all the numbers):
#5n + 20 = 310#
Subtract each side by #20#:
#5n + 20 - 20 = 310 - 20#
#5n = 290#
Now we can divide by #5#:
#(5n)/5 = 290/5#
#n = 58#
Since we know the first number, #n = 58#, and we know that the third number is #n + 4#, simply figure out what #n + 4# is:
#n + 4 = 58 + 4 = 62#
Therefore the third number in the sequence is #62#.
