A cell phone company plans to market a new smartphone. they have already sold 612 units durning the first week of the campaign. they plan to increase sales by 8% each week. for example, they plan to sell about 661 units durning week 2. they want to continue this for a year (52 weeks)

The first term is 612.

The common ratio is 1.08 and

The recursive rule is

Step-by-step explanation:

the question to the problem is to write the values of the first term, common ratio, and expression for the recursive rule.

The first term :

In geometric sequence, the first term is given as .

⇒

Now, the geometric sequence follows as 612, 661, ........

The common ratio (r) :

It is the ratio between two consecutive numbers in the sequence.

Therefore, to determine the common ratio, you just divide the number from the number preceding it in the sequence.

⇒ r = 661 divided by 612

⇒ r = 1.08

To find the recursive rule :

A geometric series is of the form  a,ar,ar2,ar3,ar4,ar5........

Here, first term and other terms are obtained by multiplying by r.

The recursive rule is of the form

This is called recursive formula for geometric sequence.

We know that r = 1.08 and = 612.

To find the second term , use the recursive rule

⇒

⇒

⇒

⇒

241 clients

Step-by-step explanation:

His problem can be solved using the principle of proportionality or rule three.

We can take advantage of the proportion between respondents who tell us the number of respondents and how many expect to go on vacation and the total number of workers, therefore:  

                         Respondents /// Whole company

Vacations                  21                          x

Total                          45                        516

then x equals:

x = (516 * 21) / (45)

x = 240.8

x = 241 clients

This means that approximately 241 clients expect to go on vacation throughout the company.