A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Sn: 1+4+7+...+(3n-2)=n(3n-1/2.

Answer for Sk: (3k-2)=k(3k-1)/2

Answer for Sk+1: (3(k+1)-2)=(k+1)(3(k+1)-1/2
simplified further: (3k+1)=3k^2+5k+2/2

Please let me know if this is correct. Thank you.

Question

A statement Sn about the positive integers is given.  Write statements Sk and Sk+1, simplifying Sk+1 completely.  Sn: 1+4+7+...+(3n-2)=n(3n-1/2.

Answer for Sk:   (3k-2)=k(3k-1)/2

Answer for Sk+1:  (3(k+1)-2)=(k+1)(3(k+1)-1/2
     simplified further:  (3k+1)=3k^2+5k+2/2

Please let me know if this is correct.  Thank you.

anonymous · Answer

Sn is actually:  1+4+7+...+(3n-2)=n(3n-1)/2

anonymous · Answer

$$1+4+7+...+(3n-2)=\frac{n(3n-1)}{2}$$ correct?

anonymous · Answer

Yes.

anonymous · Answer

Hi Satellite.  Thanks for helping again

anonymous · Answer

I'm getting the hang of the statements with the help.  Thanks again!

anonymous · Answer

i didn't really do anything, just rewrote the statement so i could read it
do you know how to replace $n$ by $k+1$ ?

anonymous · Answer

Yes.  Thanks.  (3(k+1)-2)=(k+1)(3(k+1)-1)/2
simplified further:  (3k+1)=3k^2+5k+2/2