Exercise 66 Page 269

We are given the following sequence generators and are asked to determine for which of them $447$ is a term of the sequence. If $447$ is a term of any of these sequences, then an integer value of $n$ would generate it. Therefore, we can substitute $t(n)=447$ and solve for the corresponding $n\text{-}$value. If it turns out to be a positive integer then $447$ is a term of the sequence. If not, it is not an element of the sequence. Let's try it for the first sequence. As the associated $n\text{-}$value is a positive integer, we know that $447$ is a term of the sequence. We will need to go through the same process for the remaining sequences. We can see the results of repeating this process in the table below.

Sequence generator	$t(n)=447$	$n$	Is 447 a term of the sequence?
a.	$447=5n-3$	$110$	$✓$
b.	$447=24-5n$	$\text{-}84.8$	$\times$
c.	$447=\text{-}6+3(n-1)$	$152$	$✓$
d.	$447=14-3n$	$\text{-}144.333\dots$	$\times$
e.	$447=\text{-}8-7(n-1)$	$\text{-}64$	$\times$

Therefore, $447$ is only a term for sequences a and c. In sequence a, it is the $90^{\text{th}}$ term. In sequence c, it is the $152^{\text{nd}}$ term.