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

2 answers

I think they gave you Sk
k(3k-1)/2

Sk+1 = Sk + 3 (k+1) - 2

= (3 k^2 - k)/2 + 3 k +1

= (1/2)( 3 k^2 - k + 6 k +2 )

= (1/2)(3 k^2 + 5k + 2)

= 1.5 k^2 + 2.5 k + 1
Thank you so much !