Chapter 8.2, Problem 40HP

To determine

To explain:If Edward and Alliyah are either correct or not for writing a rule for finding the $n^{th}$ term of the given sequence.

Answer to Problem 40HP

The statement is given by Edward is not true and the statement is given by Alliyah is true.

Explanation of Solution

Given information:

The sequence is,

  $14,18,22,26,\mathrm{.......}$

Edward:

The difference is 4, so the rule is $t=4n$

Alliyah:

The difference is 4 and each term is 10 more than four times the term number, so the rule is $t=4n+10$

Edward:

The difference is 4, so the rule is $t=4n$

The statement is given by Edward is not true, because when substitute $n=1$ in $n^{th}$ term formula,

  $\begin{array}{l}t=4n\\ t=4\left(1\right)\\ t=4\end{array}$

The first term is 4 but in the given sequence the first term is 14.

So, the statement is given by Edward is not true.

Alliyah:

The difference is 4, so the rule is $t=4n+10$

The statement is given by Alliyah is true, because when substitute $n=1$ in $n^{th}$ term formula,

  $\begin{array}{l}t=4n+10\\ t=4\left(1\right)+10\\ t=14\end{array}$

The first term is 14 and in the given sequence the first term is 14.

So, the statement is given by Alliyah is true.