### Home > INT3 > Chapter 9 > Lesson 9.1.2 > Problem9-23

9-23.

Consider the following three sequences:

$t(n)=50−7n$
$h(n)=4·3^n$
$q(n)=n^2−6n+17$

1. Which, if any, is arithmetic? Geometric? Neither?

$t(n)=50−7n=43,36,29...$
$h(n)=4·3n=12,36,108...$
$q(n)=n2−6n+17=12,9,8,9...$

2. Are there any terms that all three sequences have in common? Justify how you know for sure.

Continue the sequence of numbers for $q(n)$.
Are any of these numbers the same as $t(n)$ and $h(n)$?

3. Are there any terms that two of them share? Justify how you know for sure.

Set the equations equal to each other and solve for $x$.