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

9-23.

Consider the following three sequences: Homework Help ✎

*t*(*n*) = 50 – 7*n**h*(*n*) = 4 · 3^{n}*q*(*n*) =*n*^{2}– 6*n*+ 17Which, if any, is arithmetic? Geometric? Neither?

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

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

*t*(*n*) = 50 − 7*n* = 43, 36, 29...*h*(*n*) = 4 · 3* ^{n}* = 12, 36, 108...

*q*(

*n*) =

*n*

^{2}− 6

*n*+ 17 = 12, 9, 8, 9...

Continue the sequence of numbers for *q*(*n*).

Are any of these numbers the same as *t*(*n*) and *h*(*n*)?

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