Question

18 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 1

\(S_k\): replace all \(n\)'s with \(k\)'s
\(S_{k+1}\): add the \((k+1)\)-th term on the left side of the equation.. which is adding on the term (3k-2) to the end and by replacing the "k" with "k+1", and on the ride side, replace all \(k\)'s with \((k+1)\)'s