Chapter 8.2, Problem 27PPS

a.

To determine

To Find:A rule that describes a sequence of the given figure.

  

Answer to Problem 27PPS

The equation for the sequence is $t=2n+1$

Explanation of Solution

Given information:

  

Calculation:

Number of beams(n)	1	2	3
Number of traingles(t)	3	5	7

The difference of the number of beams is 1, and that of the number of triangle is 2

The pattern in the table shows the equation $t=2n+1$

b.

To determine

To Find:The number of triangles that will be formed for the frame.

  

Answer to Problem 27PPS

The required number of triangles are 55.

Explanation of Solution

Given information:

  

The frame of a new office building will use 27 beams

Calculation:

Number of beams (n)	1	2	3
Number of triangles(t)	3	5	7

The difference of the number of beams is 1, and that of the number of triangle is 2

The pattern in the table shows the equation $t=4n+1$

Using the equation to find the number of triangles in 27beams.n= 27

  $\begin{array}{c}t=2n+1\\ =2\cdot 27+1\\ =54+1\\ =55\end{array}$