Chapter 3.6, Problem 3CYU

To determine

To find the next three terms of the arithmetic sequence.

Answer to Problem 3CYU

  $0,-3,-6$

Explanation of Solution

Given:

Sequence:

  $12,9,6,\mathrm{3...}$

Concept used:

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Calculation:

The common difference of the arithmetic sequence is:

  $9-12=-3$

Now, the next three consecutive numbers are:

  $\begin{array}{l}3+(-3)=3-3=0\\ 0+(-3)=-3\\ -3+(-3)=-3-3=-6\end{array}$

Conclusion:

Therefore, the next three terms of the arithmetic sequence: $0,-3,-6$ .