Consider the sequence 1, –3, 9, –27, 81, … Which statement describes the sequence? The sequence diverges.
The sequence converges to 0.
The sequence converges to 1.
The sequence converges to ∞.

a(n)=(n-1)(-3), where n=the nth term of the sequence, n-1=the previous term, and where -3=a constant multiplier

PREMISES

1,-3,9,-27,81,…

PATTERN

This sequence follows a geometric algorithm:

a(n)=(n-1)(-3), where n=the nth term of the sequence, n-1=the previous term, and where -3=a constant multiplier

PATTERN

(1) (-1/3)×-3=1

(2) 1×-3=-3

(3) -3×-3=9

(4) 9×-3=-27

(5) -27×-3=81

(6) 81×-3=-243

(7) -243×-3=729

(8) 729×-3=-2187

(9) -2187×-3=6561

(10) 6561×-3=-19683

(100) about 9×10^42(6561)(-3)=about -177147×10^42

and so forth

C.H.

There is a similar problem with the same numbers except with no negatives so it goes 1 , 3 , 9 , 27, 81 for this question the answer is that it diverges.

Step-by-step explanation:

It was on the unit test review for edge and the answer was that it diverges.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

10

step-by-step explanation: