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.

Answer 1

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

Answer 2

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

Answer 3

Yes.

Answer 4

Hi Satellite. Thanks for helping again

Answer 5

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

Answer 6

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

Answer 7

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