A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.?

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1 Answer
KillerBunny
May 2, 2018

#S_1#: #2# is a factor of #8#
#S_2#: #2# is a factor of #18#
#S_3#: #2# is a factor of #30#

Explanation:

The general statement #S_n# claims that, whichever #n# you choose, if you compute #n^2+7n#, it will be even (i.e., 2 is a factor of that number). So, #S_1#,#S_2# and #S_3# are the same statement, written with different numbers:

#S_1#: #2# is a factor of #1^2+7*1#
#S_2#: #2# is a factor of #2^2+7*2#
#S_3#: #2# is a factor of #3^2+7*3#

Is it true? You only have to do the math: they translate into

#S_1#: #2# is a factor of #8#
#S_2#: #2# is a factor of #18#
#S_3#: #2# is a factor of #30#

which are all true.

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