Question

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true.
Sn: 2 is a factor of n2 + 7n

Answer 1

\[Sn=n ^{2}+7n\]
\[S1=1^{2}+7\times1=1+7=8=2\times4,\]
which shows S1 is true.
\[S2=2^{2}+7\times2=4+14=18=2\times9\]
which shows S2 is true.
\[S3=3^{2}+7\times3=9+21=30=2\times15\]
which shows S3 is true.
Here S1,S2,S3 are all divisible by 2 ,hence all are true.

Answer 2

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