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Damm [24]
2 years ago
9

A geometric sequence is shown below.

Mathematics
1 answer:
S_A_V [24]2 years ago
8 0

a_1=2;\ a_2=-6;\ a_3=18;\ a_4=-54;\ a_5=162;\ ...

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

A recursive rule for a geometric sequence:

a_1\\\\a_n=r\cdot a_{n-1}

r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\r=\dfrac{-6}{2}=-3

Therefore \boxed{a_1=2;\qquad a_n=-3a_{n-1}}

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

The exciplit rule:

a_n=a_1r^{n-1}

Substitute:

a_n=2(-3)^{n-1}=2(3)^n(3)^{-1}=2(3)^n\left(\dfrac{1}{3}\right)\\\\\boxed{a_n=\dfrac{2}{3}\left(-3)^n}

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Here are 180 candies in a candy shipment. There are Gobs, Blobs, and Toffees. The bage are made in ratio of 4:2:3 of Gobs, to Bl
Maru [420]

Answer:

The answer to the cost for each toffee is given below:

Step-by-step explanation:

The computation of the cost for each toffee is shown below:

Given that

There are a total 180 candies hat includes three types  in a ratio of 4:2:3

Gobs = 4 ÷ 9 × 180 = 80

Blobs = 2 ÷ 9 × 180 = 40

Toffees = 3 ÷ 9 × 180 = 60

Now the total cost of all the candies shipment is $430

So,

The equation would be

80 × $1.50 + 40 × $2.50 + 60 × per cost = $430

120 + 150 + 60 × per cost = $430

60 × per cost = $430 - $120 - $150

60 × per cost = $160

Per cost is $2.67

So for toffees it would be 160

4 0
2 years ago
the ratio of the measures of the sides of a triangle is 21:8:14. if the perimeter of the triangle is 215 ft, find the length of
Anestetic [448]

Answer:

see explanation

Step-by-step explanation:

the perimeter is the sum of the 3 sides of the triangle

add the parts of the ratio 21 + 8 + 14 = 43

divide the perimeter by 43 to find the value of one part of the ratio

\frac{215}{43} = 5 ft ← 1 part of the ratio, hence

21 parts = 21 × 5 = 105 ft

8 parts = 8 × 5 = 40 ft

14 parts = 14 × 5 = 70 ft

the 3 sides of the triangle are 105 ft, 40 ft and 70 ft


6 0
3 years ago
John needs to produce a scale diagram of a bedroom using a scale of 1:40. The length of the room is 3.4 metres. What is the leng
Varvara68 [4.7K]

Answer:

8.5cm

Step-by-step explanation:

convert 3.4metres to cm that is by multiplying by 100

3.4×100=340cm

1rep 40

?rep 340

that is 340/40

=8.5cm

5 0
3 years ago
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svetoff [14.1K]

Answer:

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Step-by-step explanation:

8 0
3 years ago
ALGEBRA Identify the similar triangles. Then find each measure.
Elena L [17]

Answer:

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Step-by-step explanation:

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2 years ago
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