Chapter 11.5, Problem 43PPS

(a)

To determine

Write a recursive Formula for the number of blue Triangles in the sequence of figure.

Answer to Problem 43PPS

Recursive Formula: $a_n=3a_{n-1};a_1=1$

Explanation of Solution

Given:

Consider the figures at the right. The number of blue triangles increases according to a specific pattern.

  

Write a recursive Formula for the number of blue Triangles in the sequence of figure.

Concept Used:

Recursive Formula: $a_n=3a_{n-1};a_1=1$

Thus, the Recursive Formula: $a_n=3a_{n-1};a_1=1$

(b)

To determine

Find the number of blue triangles in the sixth figure.

Answer to Problem 43PPS

The number of blue triangles in the sixth figure is 243.

Explanation of Solution

Given:

Consider the figures at the right. The number of blue triangles increases according to a specific pattern.

  

How many blue triangles will be in the sixth figure?

Concept Used:

Recursive Formula: $a_n=3a_{n-1};a_1=1$

Calculation:

Recursive Formula: $a_n=3a_{n-1};a_1=1$

  $\begin{array}{l}{a}_1=1\\ a_2=3a_1=3·1=3\\ a_3=3a_2=3·3=9\\ a_4=3a_3=3·9=27\\ a_5=3a_4=3·27=81\\ a_6=3a_5=3·81=243\end{array}$

Thus, the number of blue triangles in the sixth figure is 243.