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

⇒

⇒

⇒

⇒

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

12.5 feet

step-by-step explanation: