Question #1f547

1 Answer
Jan 13, 2018

Set the first number to some variable #n# and write all the other #4# numbers in terms of #n#, equate the sum to #310#, solve for #n#, then solve for the third number in terms of #n# to get #62#.

Explanation:

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#.