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3 years ago

5 pts

Mathematics

1 answer:

ruslelena [56]3 years ago

4 0

Answer:

{8, 24, 72, 216, 648}

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient of consecutive terms is always the same, that is, each term is the previous term multiplied by the common ratio.

In this question:

First element is 8, common ratio of 3. So

Second term: 8*3 = 24

Third term: 24*3 = 72

Fourth term: 72*3 = 216

Fifth term: 216*3 = 648

So the answer is {8, 24, 72, 216, 648}

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2x - 3y = 12<br> x = 4y + 1

padilas [110]

Answer:

(9,2)

Step-by-step explanation:

This is the point formula

5 0

3 years ago

I need help with this problem from the calculus portion on my ACT prep guide

LenaWriter [7]

Given a series, the ratio test implies finding the following limit:

$\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=r$

If r<1 then the series converges, if r>1 the series diverges and if r=1 the test is inconclusive and we can't assure if the series converges or diverges. So let's see the terms in this limit:

$\begin{gathered} a_n=\frac{2^n}{n5^{n+1}} \\ a_{n+1}=\frac{2^{n+1}}{(n+1)5^{n+2}} \end{gathered}$

Then the limit is:

$\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=\lim _{n\to\infty}\lvert\frac{n5^{n+1}}{2^n}\cdot\frac{2^{n+1}}{\mleft(n+1\mright)5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert$

We can simplify the expressions inside the absolute value:

$\begin{gathered} \lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert \\ \lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert=\lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert \\ \lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert=\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert \end{gathered}$

Since none of the terms inside the absolute value can be negative we can write this with out it:

$\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}$

Now let's re-writte n/(n+1):

$\frac{n}{n+1}=\frac{n}{n\cdot(1+\frac{1}{n})}=\frac{1}{1+\frac{1}{n}}$

Then the limit we have to find is:

$\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}$

Note that the limit of 1/n when n tends to infinite is 0 so we get:

$\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}=\frac{2}{5}\cdot\frac{1}{1+0}=\frac{2}{5}=0.4$

So from the test ratio r=0.4 and the series converges. Then the answer is the second option.

8 0

2 years ago

What is 3-2 2/3??????

ehidna [41]

Answer:1/3

Step-by-step explanation:

3-2 2/3 its easy because if you have 3 wholes and then only 2 2/3 of that is being taken away then you have 1/3 of 3 left over

4 0

3 years ago

How to find out the independent variable and dependent variable from a graph?

I am Lyosha [343]

Answer:

The Axes. The independent variable belongs on the x-axis the(horizontal line) of the graph and the dependent variable belongs on the y-axis the (vertical line)

6 0

3 years ago

Tell whether the sequence is arithmetic if it is identify the common difference. -7, -3, 1, 5

Oxana [17]

Step-by-step explanation:

If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

d=-7+3=-3-1=1-5=-4

so it is an arithmetic sequence

hope it helps

7 0

3 years ago