### Home > CCA2 > Chapter 3 > Lesson 3.1.2 > Problem3-26

3-26.

Find an equation for each sequence below. Then describe its graph.

1. $\left. \begin{array} { c | c } { n } & { t ( n ) } \\ \hline 3 & { 8 } \\ \hline 5 & { 2 } \\ \hline 7 & { - 4 } \\ \end{array} \right.$

First, decide if the given sequence is arithmetic or geometric.

Common difference $=$

$\frac{\Delta t(n)}{\Delta n} = \frac{2 -8 }{5 -3} = \frac{-6}{2}=-3$

So, $t(n)=−3n+b$.

Find the value of $b$ at $(3,8)$.

Write the equation once you know $b$. Then describe the graph.

$t(n)=−3n+17$

The graph is a straight line with the $y$-intercept at $(0,17)$ and a slope of $−3$.

1. $\left. \begin{array} { c | c } n & { t ( n ) } \\ \hline 1 & { 40 } \\ \hline 2 & { 32 } \\ \hline 3 & { 25.6 } \end{array} \right.$

The multiplier is less than $1$.

You will need to find $t(0)$ to write the equation.

This graph is not linear.