The sum of eight consecutive (one after the other) numbers is 88. What are the numbers?

1 Answer
mason m
Apr 17, 2016

If we call the first number, an unknown, #n#, then the next consecutive numbers are #n+1,n+2. . . n+7#.

Thus, when we add all the terms, from #n# to #n+7# together, and set that equal to #88#, we get:

#8n+28=88#

Note that #1+2+3+4+5+6+7=28#.

This gives us

#8n=60#

#n=15/2#

Note that this is not an integer, which leads us into shaky territory: its hard to define #15/2,17/2,19/2. . .# as "consecutive numbers," per se.

A more apt description of this would be that the sum of these #8# numbers, all of which are #1# away from the next highest number, have a sum of #88#.

#15/2+17/2+19/2+21/2+23/2+25/2+27/2+29/2=88#

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