PLEASE help me with this algebra II question! #5 please!

is a geometric sequence, which means consecutive terms occur in a fixed ratio. In other words,

for some fixed number .

Using this rule, we have

So, given that and , we have

We can write in terms of :

(notice how the subscript and exponent add up to ) so the sequence is given by the explicit rule

Incidentally, we can pull out the first term from this sequence by plugging in to find .

Next, if denotes the th partial sum of the sequence, then

For geometric sequences, we can replace through with terms containing :

Multiply both sides by :

Subtract from ; a bunch of terms cancel and we're left with

For the sequence at hand, plug in and . Then

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

"exterior angles = 360 / number of sides.

60 = 360 / sides

sides = 360 / 60

sides = 6"