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3 years ago

What is the explicit formula for this sequence? 2,6, 18, 54, 162, ...

Mathematics

1 answer:

allsm [11]3 years ago

8 0

Answer:

$\large\boxed{a_n=2\cdot(3)^{n-1}}$

Step-by-step explanation:

$2,\ 6,\ 18,\ 54,\ 162,\ ...\\\\2\cdot3=6\\6\cdot3=18\\18\cdot3=54\\54\cdot3=162\\\vdots\\\\\text{It's a geometric series with common ratio}\ r=3,\ \text{and the first term}\ a_1=2.\\\\\text{The explicit formula of a geometric sequence:}\ a_n=a_1r^{n-1}.\\\\\text{Substitute:}\\\\a_n=2\cdot(3)^{n-1}$

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Darcy and Harper work for different catering companies. Darcy earns a weekly salary of $982 and an 18% commission on her food

PilotLPTM [1.2K]

Answer:

$2500

Step-by-step explanation:

Given that:

Darcy's weekly earning = $982 plus 18% commission on food sales

Harper's weekly earning = $807 plus 25% commision

amount of food sales will result in Darcy and Harper earning the same amount for the week

Let amount of food sales = f

Darcy's earning = Harper's earning

(982 + 18%*f) = (807 + 25% * f)

(982 + 0.18f) = (807 + 0.25f)

982 + 0.18f = 807 + 0.25f

982 - 807 = 0.25f - 0.18f

175 = 0.07f

f = 175 / 0.07

f = 2500

Hence amount of food sales that will result in both Darcy and Harper earning the same amount = $2500

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4 years ago

Sarah had 1/2 gallon of ice cream and wants to divide it into one cup servings to share with her class. A cup is one-sixteenth o

sergey [27]

She needs 8 serving dishes because you can only make 8 one cup servings out of a half gallon of ice-cream.

6 0

4 years ago

What is the value of x? 4 8 6 10

dsp73

Answer:

The right answer for the question is 6.

8 0

2 years ago

Find x.................

Mkey [24]

Two the smaller right angled triangles are similar. Therefore:
$\dfrac{x}{3}=\dfrac{3}{2}\ \ \ |\cdot3\\\\x=\dfrac{9}{2}\\\\\boxed{x=4.5}$

Answer: a) 4.5

8 0

3 years ago

The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$

babymother [125]

You're given

x + y + z = 165

7x = n

n = y - 9

n = 9 + z

and you want to find xyz.

Solve the last three equations for x, y, and z :

7x = n → x = n/7

n = y - 9 → y = n + 9

n = 9 + z → z = n - 9

Substitute x, y, and z into the first equation and solve for n :

n/7 + (n + 9) + (n - 9) = 165

n/7 + 2n = 165

n + 14n = 1155

15n = 1155

n = 77

Now solve for x, y, and z :

x = 77/7 = 11

y = 77 + 9 = 86

z = 77 - 9 = 68

Then the product is

xyz = 11 • 86 • 68 = 64,328

6 0

3 years ago