Thinking Mathematically (6th Edition)

$\underline{Inductive\ Reasoning}$ Each result in the sequence is a number that is one digit longer than the prior result. The leading digit is one greater than the prior leading digit. All other positions contain the digit 8. We therefore induce that the next result will be 488,888. $\underline{Check\ Computation}$ Each computation includes 2 factors and an minuend. The first factor is one digit longer than the first factor in the prior item in the sequence and contains the same trailing digits as those in the first factor in the prior item in the sequence. The new leading digit contains a value one greater than the leading digit in prior item in the sequence. $1\rightarrow21\rightarrow321\rightarrow4321\rightarrow54321$ The first factor in the next computation in the sequence will therefore be 54321. The second factor is 9 for every computation in the sequence. The minuend is 1 for every computation in the sequence. The next computation in the sequence is $54321\times9-1=488889-1=488888$ This result agrees with the result derived by inductive reasoning.