MATHEMATICS COLLEGE

Consider the sequence below. 3, 1, 1/3, 1/9,...

select the explicit function which defines the sequence.

A.) f(n) = 1/3 • 2^(n - 1)

B.) f(n) = 2 • (1/3)^(n - 1)

C.) f(n) = 1/3 • 3^(n - 1)

D.) f(n) = 3 • (1/3)^(n - 1)

Answers

Answer 1
Answer: ANSWER

The explicit formula that defines the sequence is
f(n) = 3 ( (1)/(3) ) ^(n - 1)


EXPLANATION


The given sequence is
3,1, (1)/(3) , (2)/(9) ,...


The first term of this sequence is
a = 3
We can find the common ratio by expressing a subsequent term over a previous term and simplifying it.


The common ratio is
r = (1)/(3)


The formula for finding the nth term of the given geometric sequence is given by,

f(n) = a {r}^(n - 1)




We now substitute the value of the first term and the common ratio in to the above formula to obtain,



f(n) = 3( (1)/(3) )^(n - 1)


The correct answer is option D.
Answer 2
Answer:

Answer:

D

Step-by-step explanation:

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Answers

Answer:

Step-by-step explanation:

Hope this helps u !!

Answer:

first thing B union with c { 2,3,4,5,6}

then this group intersect with A that's will be {1,2,3} intersect with { 2,3,4,5,} the result { 2,3}

Ls i cant figure it out quick please

Answers

Answer:

1479 g

Step-by-step explanation:

The volume of the bar is

V = l*w*h

  = 10*3*5

  = 150 cm^3

Now multiply by the density

150 cm^3 * 9.86 g/ cm^3 =1479 g

The set of all real numbers x that satisfies -3 < x<14 is given by the following interval notation: [-3,14) True or False?

Answers

Answer: it’s false

Step-by-step explanation:

I just took the test and got it right :)

Answer:

Step-by-step explanation:

The set of all integer numbers

Baby Unicorns have a weekly training schedule, flying for 4 hours per day on some days and 2 hours per day on the other days. They fly a total of 24 hours in a seven-day week. On how many days do they fly for 4 hours?

Answers

The Baby unicorns fly 4 hours for 5 days and 2 hours for 2 days.

Let x represent the number of days flown 4 hours and y represent the number of days flown 2 hours

Since they worked a total of 7 days, hence:

x + y = 7     (1)

Also, they flew for 24 hours hence:

4x + 2y = 24   (2)

Solving equations 1 and 2 simultaneously gives:

x = 5, y = 2

Therefore they fly 4 hours for 5 days and 2 hours for 2 days.

Find out more at: brainly.com/question/16763389

Which expression is equivalent to 3/ x^5y
\sqrt[3]{ {x}^(5)y }
​

Answers

Answer:

{x}^{ (5)/(3) } {y}^{ (1)/(3) }

Step-by-step explanation:

A cube root is equivalent to the power of 1/3, so by taking the powers of the exponents and multiplying them by 1/3, you get your answer.

Answer:

\sqrt[3]{x^5 \ y } = (x^5 y)^(1)/(3) = x^{ (5)/(3)} \ y^ { (1)/(3)}

Find the equation of a line passing through the point (-4,1) and perpendicular to theline 3y = 12x - 9.

Answers

Answer:

A. y=-1/4x

Step-by-step explanation:

We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.
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