Q57. - Algebra 2

Question

WRITING IN MATH

Answer the question that was posed at the beginning of the lesson. 

How are arithmetic sequences related to roofing?

Include the following in your answer:

• the words that indicate that the numbers of shingles in the rows form an

arithmetic sequence, and

• explanations of at least two ways to find the number of shingles in the

fifteenth row.

Step-by-Step Solution

Answer

• One additional shingle is needed in each successive row.
• One way is to add one in successive row and other is to use formula 
• $a_n=a+(n-1)d$
  

Step 1. Given information

Arithmetic sequencing with roofing

Step 2. Concept used

We need one additional shingle to indicate the number of shingles.

There are two ways described in calculation part.

Step 3. Calculation

One method is to successively add 1 to the terms of the sequence: 

$\begin{array}{l}{a}_8=9+1=10,\\ a_9=10+1=11,\\ a_{10}=11+1=12,\\ a_{11}=12+1=13,\\ a_{12}=13+1=14,\\ a_{13}=14+1=15,\\ a_{14}=15+1=16,\\ a_{15}=16+1=17.\end{array}$

Another method is to use the formula for the nth term:${\text{a}}_{15}\text{=3+(15-1) =17}$