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3 years ago

Find the pattern and use it to list the nth term in the sequence. 3, 9, 27, 81, 243 ...

Mathematics

1 answer:

KonstantinChe [14]3 years ago

3 0

The pattern is formed a geometric sequence

The nth term of the sequence is $a_{n}=3^{n}$

Step-by-step explanation:

The formula of the nth term of a geometric sequence is:

$a_{n}=ar^{n-1}$ , where

a is the first term
r is the common ratio between the consecutive terms

∵ The pattern is 3 , 9 , 27 , 81 , 243

∵ 9 ÷ 3 = 3

∵ 27 ÷ 9 = 3

∵ 81 ÷ 27 = 3

∵ 243 ÷ 81 = 3

- There is a common ratio 3 between each two consecutive terms

∴ The pattern is formed a geometric sequence

∵ The first term is 3

∴ a = 3

∵ The common ratio is 3

∴ r = 3

- To find the nth term substitute a and r in the formula above

∵ $a_{n}=ar^{n-1}$

∴ $a_{n}=3(3)^{n-1}$

- Remember we add the powers of the same base with multiplication

∵ 3 × $3^{n-1}$ = $3^{1+n-1}$

∴ 3 × $3^{n-1}$ = $3^{n}$

∴ $a_{n}=3^{n}$

∴ The nth term of the sequence is $a_{n}=3^{n}$

Learn more:

You can learn more about the sequences in brainly.com/question/1522572

#LearnwithBrainly

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3m+3n=36 8m+5n=31 Using the process of elimination

amm1812

Answer:

m=-29/3 and n=65/3

Step-by-step explanation:

The given system has equations:

3m+3n=36

8m+5n=31

Multiply the top equation by 5 and bottom equation by 3 to get:

15m+15n=180

24m+15n=93

Subtract the top equation from the bottom equation to get:

9m=-87

Divide both sides by 9

$m = - \frac{29}{3}$

We substitute this value into the first equation to get:

$3( - \frac{29}{3} ) + 3n = 36$

$3n = 36 + 29$

$3n = 65$

$n = \frac{65}{3}$

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3 years ago

BRAINLIEST..........show expressions too<333

vovikov84 [41]

Answer:

9.) $t=.05m+20$

10.) $t=.10m+5$

11.) $300$ minutes of calling would make the two plans equal.

12.) Company B.

Step-by-step explanation:

Let t equal the total cost, and m, minutes.

Set up your models for questions 9 & 10 like this:

total cost = (cost per minute)# of minutes + monthly fee

Substitute your values for #9:

$t=.05m+20$

Substitute your values for #10:

$t=.10m+5$

To find how many minutes of calling would result in an equal total cost, we have to set the two models we just got equal to each other.

$.10m+5=.05m+20$

Let's subtract $5$ from both sides of the equation:

$.10m=.05m-15$

Subtract $.05m$ from both sides of the equation:

$.05m=15$

Divide by the coefficient of $m$ , in this case: $.05$

$m=300$

Let's substitute $200$ minutes into both of our original models from questions 9 & 10 to see which one the person should choose (the cheaper one).

Company A:

$t=.05(200)+20$

Multiply.

$t=10+20$

Add.

$t=30$

Company B:

$t=.10(200)+5$

Multiply.

$t=20+5$

Add.

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3 years ago

(17 PTS) GEOMETRY QUESTIONS, PLEASE HELP!

nekit [7.7K]

14.
Angles 4 and 6 are supplementary, because they are on the same line. Supplementary angles add up to 180 degrees, and a line must be 180 degrees.

15.
Angles 1 and 8 are congruent, because they are alternate exterior angles

16.
m = y2 - y1 / x2 - x1
m = 7 - 2 / 4 - 5
m = 5 / -1
m = -5

17.
m = 3 - 3 / 7 - (-5)
m = 0 / 12
m = 0

18.
m = 1 - (-2) / 5 - (-4)
m = 3 / 9
m = 1/3

19.
A = (0, 3) - B = (3,0)
m = 0 - 3 / 3 - 0
m = -3 / 3
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20.
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m = -2 / -1
m = 2
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21.
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m = -4 - 1 / 2 - 0
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Perpendicular, because the slopes are opposite reciprocals.

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Horizontal line
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23.
Angle 2 is congruent to angle 1 because of the alternate exterior angle theorem.
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Angle 2 is congruent to angle 3 because of substitution.
Line l is parallel to line m because the corresponding angles are congruent.

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3 years ago

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3 years ago

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Answer:

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Step-by-step explanation:

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