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5-136. This problem is a checkpoint for writing equations for arithmetic and geometric sequences. It will be referred to as Checkpoint 5B.

1. Write an explicit and recursive rule for $t(n)=1,4,7,10,\ \dots$

2. Write an explicit and recursive rule for $t(n)=3,\frac{3}{2},\frac{3}{4},\frac{3}{8},\dots$
In parts (c) and (d), write an explicit rule for the sequence given in the $n→t(n)$ tables.

1. An arithmetic sequence

$\begin{array}{c|c} \quad n\quad & \; t(n) \;\\ \hline 1 & 17\\ \hline 2 & \\ \hline 3 & 3\\ \hline 4 & \end{array}$

1. A geometric sequence

$\begin{array}{c|c} \quad n\quad & \;\; t(n) \;\; \\ \hline 1 & \\ \hline 2 & 7.2\\ \hline 3 & 8.64\\ \hline 4 & \end{array}$

1. If an arithmetic sequence has $t(7)=1056$ and $t(12)=116$, what is $t(4)$?

Check your answers by referring to the Checkpoint 5B materials located at the back of your book.

Ideally, at this point you are comfortable working with these types of problems and can solve them correctly. If you feel that you need more confidence when solving these types of problems, then review the Checkpoint 5B materials and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.

Answers and extra practice are located in the back of your printed textbook or in the Reference Tab of your eBook.
If you have an eBook for CCG, login and then click the following link: Checkpoint 5B: Writing Equations for Arithmetic and Geometric Sequences