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Lorico [155]
3 years ago
9

What is the explicit rule for this geometric sequence? 2, 6, 18, 54, …

Mathematics
1 answer:
Alex787 [66]3 years ago
6 0

Answer:

A term at position n can be expressed as \[2*3^{n-1}\]

Step-by-step explanation:

The given geometric sequence is 2, 6, 18, 54, …

Starting term = 2

Second term = 6

So second term is 3 times the first term.

Similarly, Third term = 18

This is 3 times the second term, that is , 3 * 6

Fourth term is is 54.

This is 3 times the third term, that is , 3 * 18

Generalizing, a term in the sequence can be expressed as \[2*3^{n-1}\]

where n represents the position of the term in the sequence.

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Two triangles are similar.The the smaller triangle has side 10,20 and 15 units the larger triangles longest side is 52 units.Wha
Oliga [24]

Answer: The perimeter of the largest triangle = 117 units.

Step-by-step explanation:

Sides of smaller triangle = 10,20 and 15 units

Longest side = 20 units

Longest side of larger triangle = 52 units

Sides of two similar triangles are proportional.

Let k be proportionality constant.

k=\dfrac{\text{Length in larger triangle}}{\text{Length in smaller triangle}}

k=\dfrac{52}{20}\\\\\Rightarrow\ k=\dfrac{13}{5}

Length of other two sides,

10\times\dfrac{13}{5}, 15\times\dfrac{13}{5}\ i.e.\ 26\text{ units}, 39\text{ units.}

So sides of larger triangle = 52 units, 26 units , 39 units

Perimeter of largest triangle = 52 +26+39 = 117 units

Hence, the perimeter of the largest triangle = 117 units.

4 0
3 years ago
Please help!!!!! thank u!!
Naddika [18.5K]
Set each piece = to 56, assuming that the 2 variables for which you are not solving are each equal to 0.

7x -2(0)-14(0) = 56
7x=56 (divide each side by 7)
X = ?
(__, 0, 0)

7(0) - 2y - 14 (0) = 56
-2y = 56 (divide each side by -2)
Y= ?
(0, __ , 0)

7(0) - 2(0) - 14z = 56
-14z = 56 (divide each side by -14)
z = ?
(0, 0, __)
4 0
3 years ago
I don't quite understand the LCD and the unlike denominators properly. May someone explain it, please.
Whitepunk [10]

Hey!

----------------------------------------------------------------------

LCD stands for Lowest Common Denominator.

----------------------------------------------------------------------

Explanation:

So let's say we have the equation 1/9 * 16/27

We want to find the LCD of both fractions. To find the LCD of both fractions find a the lowest common denominator in both fractions.

In this equation the lowest common denominator is 27 because 9 can go in 27 and 27 can go into itself. Se basically 27 is the lowest possibly common denominator both fractions can get to.

----------------------------------------------------------------------

Hope This Helped! Good Luck ;)

5 0
3 years ago
Help please! tyssssm!
Lubov Fominskaja [6]

Answer:

B. Negative

⁄(⁄ ⁄•⁄ω⁄•⁄ ⁄)⁄

8 0
3 years ago
Read 2 more answers
A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m 24 m24, start text, space,
Alchen [17]

Answer:

24(\frac{1}{2})^{n-1}

Step-by-step explanation:

<u>Complete Question:</u>

A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m. With each swing, she travels along an arc that is half as long as the arc of the previous swing. Which expression gives the total length the monkey swings in her first n swings?

<u>Solution:</u>

First Swing:

24 m

Second Swing:

Half of first, so

24(1/2)

Third Swing:

Half of second, so:

24(1/2)(1/2)

Fourth Swing:

24(1/2)(1/2)(1/2)

So we see the general formula as:

24(\frac{1}{2})^{n-1}

<u>Note:</u> n -1 because (1/2) plays a role from second swing, which is n - 1

where n is the number of swings

7 0
3 years ago
Read 2 more answers
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