Chapter 11.4, Problem 73STP

(a)

To determine

Find the first eight terms of the sequence that describes the total number of squares that have been made after each meeting.

Answer to Problem 73STP

The first eight terms of the sequence are: 9, 18, 27, 36, 45, 54, 63, 72,

Explanation of Solution

Given:

A quilting club of 9 members, every week, and each member must bring one completed quilt square.

Find the first eight terms of the sequence that describes the total number of squares that have been made after each meeting.

Concept Used:

The first eight terms of the sequence are: 9, 18, 27, 36, 45, 54, 63, 72,

Calculation:

Thus, the first eight terms of the sequence are: 9, 18, 27, 36, 45, 54, 63, 72,

(b)

To determine

Find the number of meetings.

Answer to Problem 73STP

Number of meeting = 42

Explanation of Solution

Given:

A quilting club of 9 members, every week, and each member must bring one completed quilt square.

One particular quilt measures 72 inches by 84 inches and is being designed with 4 − inch squares. After how many meetings will be quilt be complete?

Concept Used:

The number of squares requires is $\frac{72·84}{4·4}=378$

So we can write $a_n=378$

Calculation:

The number of squares requires is $\frac{72·84}{4·4}=378$

So we can write: $a_n=378;\text{Given}:a_1=9;\text{and}d=9;\text{Find}n$

  $\begin{array}{l}{a}_n=a_1+(n-1)·d\\ 378=9+(n-1)·9\\ 378=9+9n-9\\ 378=9n\\ \frac{9n}{9}=\frac{378}{9}\\ n=42\end{array}$ Number of meeting = 42.

Thus, number of meeting = 42