Chapter 8.4, Problem 29SR

To determine

To write: an expression about the pattern and find the figure which will have 45 squares.

Answer to Problem 29SR

The equation of sequence is $t=4n+1$

The figure that contains 45 squares

Explanation of Solution

Given:

  

Calculation:

Consider the sequence $:5,9,13,\dots$

In the sequence, the terms have common difference of 4.

And, a term is 1 more than four times the term number. It means that the equation of sequence is:

  $t=4n+1$

So, put the value of $t=45$ in equation to find the figure number that contains 45 squares.

  $45=4n+1$

Subtract both sides of equation by 1.

  $\begin{array}{l}45-1=4n+1-1\\ 44=4n\end{array}$

Divide both sides of equation by 4.

  $\begin{array}{l}\frac{44}{4}=\frac{4n}{4}\\ 11=n\end{array}$

Conclusion:

Therefore, the figure that contains 45 squares andthe equation of sequence is $t=4n+1$