Chapter 4.6, Problem 12E

To determine

To write: The next three terms of the given arithmetic sequence.

Answer to Problem 12E

The next three terms are $45,56,67.$

Explanation of Solution

Given information: An arithmetic sequence $1,12,23,34,\mathrm{...}$ is given.

Calculation:

Arranging the given data in a table,

  $\begin{array}{lllll}Position\hfill & 1\hfill & 2\hfill & 3\hfill & 4\hfill \\ Term\hfill & 1\hfill & 12\hfill & 23\hfill & 34\hfill \end{array}$

The difference between the each pair of consecutive terms is $11$ , writing next three terms in table,

  $\begin{array}{llllllll}Position\hfill & 1\hfill & 2\hfill & 3\hfill & 4\hfill & 5\hfill & 6\hfill & 7\hfill \\ Term\hfill & 1\hfill & 12\hfill & 23\hfill & 34\hfill & 45\hfill & 56\hfill & 67\hfill \end{array}$

Thus, the next three terms are $45,56,67.$